{"id":23130,"date":"2023-02-01T06:49:23","date_gmt":"2023-02-01T06:49:23","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=23130"},"modified":"2026-05-25T11:19:33","modified_gmt":"2026-05-25T11:19:33","slug":"transitive-property","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property","title":{"rendered":"Transitive Property"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-1880c40e-9b4f-4421-ba3a-8ca6fa54f75d\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property#0-transitive-property-introduction>Transitive Property: Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property#1-transitive-property-definition>Transitive Property: Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property#8-when-do-we-use-transitive-property>When Do We Use Transitive Property?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property#15-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property#16-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property#17-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 id=\"0-transitive-property-introduction\" class=\"wp-block-heading eplus-wrapper\">Transitive Property: Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Transitive property refers to a property by which if number a is related to the number b by a certain rule, and the number b is related to the number c by the same rule, then we can definitely say that the number a is related to the number c by the same rule.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s understand this using an example. Suppose Alex has $\\$10$ in the piggy bank. Joy has the same amount in the piggy bank as Alex. George has the same amount of money as Joy. What does this imply? It\u2019s simple! It means Alex and George have the same amount of money, $\\$10$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"566\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-example.png\" alt=\"Transitive property example\" class=\"wp-image-36989\" title=\"Transitive property example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-example-300x274.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-using-associative-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_together_we_flee_4_gm.png\" alt=\"Add Using Associative Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Using Associative Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/apply-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_mul_dispro_exp1_pt.png\" alt=\"Apply Distributive Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Apply Distributive Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/multiply-using-the-commutative-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_mul_compro_fact2_pt.png\" alt=\"Multiply using the Commutative Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Multiply using the Commutative Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/solve-using-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_mul_dispro_pProd_pt.png\" alt=\"Solve using Distributive Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Solve using Distributive Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 id=\"1-transitive-property-definition\" class=\"wp-block-heading eplus-wrapper\">Transitive Property: Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us understand transitive property meaning in depth.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The word transitive means to transfer. If x, y and z are any three quantities, and if x is related to y by some rule and y is related to z by the same rule, then we can conclude that x and y are related to each other by the same rule. This property is known as the transitive property of equality.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"400\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property.png\" alt=\"Transitive property\" class=\"wp-image-36991\" title=\"Transitive property\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-300x194.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s take another example. Suppose an apple weighs the same as an orange. An orange weighs the same as a banana. Then we can say that the apple weighs the same as the banana.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"415\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-example-in-real-life.png\" alt=\"Transitive property example in real life\" class=\"wp-image-36992\" title=\"Transitive property example in real life\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-example-in-real-life.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-example-in-real-life-300x201.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-addition.jpeg\" alt=\"Add the Numbers Using Commutative Property of Addition\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-commutative-property-of-addition.jpeg\" alt=\"Apply Commutative Property of Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-commutative-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-commutative-property.jpeg\" alt=\"Apply Commutative Property Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-distributive-property-in-2-different-ways\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-distributive-property-in-2-different-ways.jpeg\" alt=\"Apply Distributive Property in 2 Different Ways Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-the-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-the-commutative-property-of-addition.jpeg\" alt=\"Apply the Commutative Property of Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/break-it-down-using-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-it-down-using-distributive-property.jpeg\" alt=\"Break it Down using Distributive Property Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/break-multiply-add-using-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-multiply-add-using-distributive-property.jpeg\" alt=\"Break Multiply Add using Distributive Property Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/break-using-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-using-distributive-property.jpeg\" alt=\"Break using Distributive Property Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/commutative-property-of-addition-on-number-line\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/commutative-property-of-addition-on-number-line.jpeg\" alt=\"Commutative Property of Addition on Number Line Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/commutative-property-of-addition.jpeg\" alt=\"Commutative Property of Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 id=\"2-what-is-the-transitive-property-of-equality\" class=\"wp-block-heading eplus-wrapper\">What Is the Transitive Property of Equality?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The transitive property of equality states that:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $\\text{x} = \\text{y}$ and $\\text{y} = \\text{z}$, then $\\text{x} = \\text{z}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The definition of the transitive property of equality by Euclid is simple. He defines it as \u201cthings which are equal to the same thing are also equal to each other.\u201d<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"487\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-of-equality.png\" alt=\"Transitive property of equality\" class=\"wp-image-36993\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-of-equality.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-of-equality-300x235.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s also explore two properties of equality that are closely related to the transitive property of equality.<\/p>\n\n\n\n<h3 id=\"3-reflexive-property-of-equality-\" class=\"wp-block-heading eplus-wrapper\"><strong>Reflexive Property of Equality<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The reflexive property states that $x = x$ for any real number $x$. Thus, any variable is always equal to itself.<\/p>\n\n\n\n<h3 id=\"4-symmetric-property-of-equality-\" class=\"wp-block-heading eplus-wrapper\"><strong>Symmetric Property of Equality<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the symmetric property of equality, if $x = y$, then $y = x$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the order in which two variables are equated, LHS or RHS, does not matter.<\/p>\n\n\n\n<h2 id=\"5-transitive-property-of-inequality\" class=\"wp-block-heading eplus-wrapper\">Transitive Property of Inequality<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Transitive property applies to equality as well as inequality and it states that, if we have three real numbers a, b, and c such that, $a \\lt b$ and $b \\lt c$, then $a \\lt c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Transitive property can also be applied to other inequalities, such $as \\gt$, $\\le$ and $\\ge$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, if we have a number $p \\le 15$ and $15 \\le q$, then $p \\le q$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us look at another example. Roy is shorter than Jim. Jim is shorter than Mike. According to the transitive property of inequality, we can say that Roy is shorter than Mike.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"456\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-of-inequality.png\" alt=\"Transitive property of inequality\" class=\"wp-image-36994\" title=\"Transitive property of inequality\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-of-inequality.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-of-inequality-300x221.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 id=\"6-transitive-property-of-congruence\" class=\"wp-block-heading eplus-wrapper\">Transitive Property of Congruence<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The definition of transitive property of congruence can be given as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If two shapes are congruent to a third shape, then all the shapes are congruent among each other.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us consider three triangles, $\\Delta ABC, \\Delta PQR$, and $\\Delta MNO$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The transitive property of congruence is given as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $\\Delta ABC \\Cong \\Delta PQR$ and $\\Delta PQR \\Cong \\Delta MNO$, then $\\Delta ABC \\Cong \\Delta MNO$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It clearly means that the triangle ABC is congruent to triangle PQR, and triangle PQR is congruent to triangle MNO, then we can say that the triangle ABC is congruent to the triangle MNO.<\/p>\n\n\n\n<h2 id=\"7-general-formula-of-transitive-property\" class=\"wp-block-heading eplus-wrapper\">General Formula of Transitive Property<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula of transitive property of equality is given as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $a = b$ and $b = c$, then $a = c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For any real numbers, a, b and c, the transitive property of inequalities states that:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $a \\lt b$ and $b \\lt c$, then $a \\lt c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $a \\gt b$ and $b \\gt c$, then $a \\gt c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $a \\le b$ and $b \\le c$, then $a \\le c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $a \\ge b$ and $b \\ge c$, then $a \\ge c$.<\/p>\n\n\n\n<h2 id=\"8-when-do-we-use-transitive-property\" class=\"wp-block-heading eplus-wrapper\">When Do We Use Transitive Property?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The transitive property in geometry is used when we are dealing with quantities following the same rule. It uses a comparison mechanism to find the values of variables. Transitive property can be applied to numbers, algebraic expressions, congruent angles, triangles, etc. It connects multiple equal quantities and thus has applications in arithmetic, logic, and algebra.<\/p>\n\n\n\n<h3 id=\"9-transitive-property-of-angles-\" class=\"wp-block-heading eplus-wrapper\"><strong>Transitive Property of Angles<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the transitive property of congruence, if $\\angle A$ is congruent to $\\angle B; \\angle B$ is congruent to $\\angle C$, then $\\angle A$ is congruent to $\\angle C$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: If we have angles a and b such that $\\angle A = \\angle B$ and $\\angle B = \\angle C$ and $\\angle A = 60^{\\circ}$, then by the transitive property of angles, we get $\\angle C = 60^{\\circ}$.<\/p>\n\n\n\n<h3 id=\"10-transitive-property-of-parallel-lines-\" class=\"wp-block-heading eplus-wrapper\"><strong>Transitive Property of Parallel Lines<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If line a is parallel to line b, and line b is parallel to line c, then we can say that line a is also parallel to line c.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"384\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-in-parallel-lines.png\" alt=\"Transitive property in parallel lines\" class=\"wp-image-36995\" title=\"Transitive property in parallel lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-in-parallel-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/transitive-property-in-parallel-lines-300x186.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 id=\"11-transitive-property-of-inequality-of-real-numbers-\" class=\"wp-block-heading eplus-wrapper\"><strong>Transitive Property of Inequality of Real Numbers<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In mathematics, inequalities are just as important as equalities. We know that the transitive property also applies to inequalities such that:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $a \\lt b$ and $b \\lt c$, then $a \\lt c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To visualize this property, consider three people whose weights are unknown. It is known that Mike is shorter than Oscar and that Oscar is shorter than David. Logic allows the conclusion that Mike is also shorter than David.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This property works in the reverse order as well: $a \\gt b$ and $b \\gt c$ then $a \\gt c$.<\/p>\n\n\n\n<h2 id=\"12-construction-of-equilateral-triangle-using-transitive-property\" class=\"wp-block-heading eplus-wrapper\">Construction of Equilateral Triangle using Transitive Property<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Transitive property is an axiom, i.e., a statement that is self-evident and accepted without proof. The construction of an equilateral triangle using a ruler and a compass is a popular example where transitive property is used.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 1: Draw line segment PQ with any measurement.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 2: Draw one circle keeping center P and radius PQ. Draw another circle with the center Q and radius QP.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 3: Name the point of intersection of two circles as R. Join PQR to form a triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As we know, PQ and PR are the radii of the circle with P as the center.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PQ = PR$ (see red circle).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PQ and QR$ are the radii of the circle with Q as the center.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PQ = QR$ (see blue circle).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since $PQ = PR$ and $PQ = QR$, we can say $PR = QR$ according to the transitive property of equality. Therefore, all three lines are equal to each other making PQR an equilateral triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"540\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-transitive-property.png\" alt=\"Proof of transitive property\" class=\"wp-image-36996\" title=\"Proof of transitive property\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-transitive-property.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-transitive-property-300x261.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<h2 id=\"13-fun-facts\" class=\"wp-block-heading eplus-wrapper\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\">The transitive property of equality : If $x = y$ and $y = z$, then $x = z$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">This property can be applied to algebraic expressions, numbers, and various geometrical concepts like congruent angles, triangles, etc.<\/li>\n<\/ul>\n\n\n\n<h2 id=\"14-conclusion\" class=\"wp-block-heading eplus-wrapper\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about transitive property. We got to know about the transitive property of equality and inequality. We also discussed formulas and now we can solve practice problems to better understand transitive property.<\/p>\n\n\n\n<h2 id=\"15-solved-examples\" class=\"wp-block-heading eplus-wrapper\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. What is the value of <\/strong>$\\text{x}$<strong>, if <\/strong>$x = y$<strong> and <\/strong>$y = 5$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By using the transitive property, if $x = y$ and $y = 5$, then $x = 5$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the value of $x$ is $5$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. What is the value of t, if <\/strong>$t + 3 = u$<strong> and <\/strong>$u = 9$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By using the transitive property, if $t + 3 = u$ and $u = 9$, then<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$t + 3 = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow t = 9 \u2212 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow t = 9 \u2212 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow t = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the value of t is 6.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Find the value of <\/strong>$\\angle R$<strong>, if <\/strong>$\\angle P = \\angle Q$<strong> and <\/strong>$\\angle Q = \\angle R$<strong>, where <\/strong>$\\angle P = 120^{\\circ}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By using the transitive property of angles,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $\\angle P = \\angle Q$ and $\\angle Q = \\angle R$ then automatically, $\\angle P = \\angle R$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the value of&nbsp; $\\angle P = \\angle R = 120^{\\circ}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Find the value of <\/strong>$\\angle R$<strong>,<\/strong> if $\\angle P + 60^{\\circ} = \\angle Q$ and $\\angle Q = \\angle R$<strong>, where <\/strong>$\\angle P = 120^{\\circ}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By using the transitive property of angles,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $\\angle P&nbsp; + 60^{\\circ} = \\angle Q$ and $\\angle Q = \\angle R$ then automatically, $\\angle P&nbsp; + 60^{\\circ} = \\angle R$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the value of&nbsp; $\\angle P&nbsp; + 60^{\\circ} = \\angle R$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Or $120^{\\circ} +&nbsp; + 60^{\\circ} =\\angle R$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Or $<strong>\\angle <\/strong>R = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the value of&nbsp; $\\angle R = 180^{\\circ}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. Assume that <\/strong>$3x + 3 = b$<strong> and <\/strong>$b = 5x \u2212 1$<strong>. What is the value of b?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this transitive property example the solution uses the transitive property of equalities to set $3x + 3$ equal to $5x \u2212 1$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $3x + 3 = 5x \u2212 1$. Solving for x results in $\u2212 2x = \u2212 4$; thus $x = 4\/2= 2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the value of $x$ is $2$.<\/p>\n\n\n\n<h2 id=\"16-practice-problems\" class=\"wp-block-heading eplus-wrapper\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Transitive Property<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the value of a, if $a = b$ and $b = 7$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4<\/div><div class=\"spq_answer_block\" data-value=\"1\">5<\/div><div class=\"spq_answer_block\" data-value=\"2\">6<\/div><div class=\"spq_answer_block\" data-value=\"3\">7<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 7<br\/>By using the transitive property, if $a = b$ and $b = 7$, then $a = 7$.<br>\r\nTherefore, the value of a is $7$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the value of t, if $m + 2 = n$ and $n = 3$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>By using the transitive property, if $m + 2 = n$ and $n=3$, then<br>\r\n$\\Rightarrow m + 2 = n$<br>\r\n$\\Rightarrow m= n$ $-$ $2$<br>\r\n$\\Rightarrow m = 3$ $-$ $2$<br>\r\n$\\Rightarrow m = 1$<br>\r\nThe value of m is 1.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the value of $\\angle A$, if $\\angle B = \\angle C$ and  $\\angle C = \\angle A$, and $\\angle B = 45^{\\circ}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$45^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$60^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$75^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$90^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $45^{\\circ}$<br\/>By using the transitive property of angles,<br>\r\nIf $\\angle B = \\angle C$ and $\\angle C = \\angle A$ then automatically, $\\angle B = \\angle A$.<br>\r\nTherefore, the value of  $\\angle B = \\angle A = 45^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">At what value of $\\angle A$, if $\\angle B + 45^{\\circ} = \\angle C$ and $\\angle C = \\angle A$, where $\\angle B = 45^{\\circ}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$45^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$60^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$75^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$90^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $90^{\\circ}$<br\/>If $\\angle B  + 45^{\\circ} = \\angle C$ and $\\angle C = \\angle A$ then automatically, $\\angle B  + 45^{\\circ} = \\angle A$.<br>\r\nTherefore, the value of  $\\angle B  + 60^{\\circ} = \\angle A$ <br>\r\nOr $45^{\\circ} +  + 45^{\\circ} = \\angle A$ <br>\r\nOr $\\angle A = 90^{\\circ}$<br>\r\nTherefore, the value of  $\\angle A = 90^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Assume that $3x + 3 = b$ and $b = 5x$ $-$ 1$. What is the value of b?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$-2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-12$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-6$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$-16$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $-16$<br\/>In this transitive property example the solution uses the transitive property of equalities to set $5x + 7$ equal to $4x$ $-$ $9$.<br>\r\nThus, $5x + 7 = 4x$ $-$ $9$. Solving for x results in<br>\r\n$5x + 7 = 4x$ $-$ $9$<br>\r\nOr $5x$ $-$ $4x = $$-$$9$ $-$$7$<br>\r\nOr $x = $$-$ $16$<br>\r\nThe value of x is $-16$.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Transitive Property\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Transitive Property\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple 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\"text\": \"By using the transitive property, if $$a = b$$ and $$b = 7$$, then $$a = 7$$.<br>\r\nTherefore, the value of a is $$7$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property, if $$a = b$$ and $$b = 7$$, then $$a = 7$$.<br>\r\nTherefore, the value of a is $$7$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property, if $$a = b$$ and $$b = 7$$, then $$a = 7$$.<br>\r\nTherefore, the value of a is $$7$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"7\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"By using the transitive property, if $$a = b$$ and $$b = 7$$, then $$a = 7$$.<br>\r\nTherefore, the value of a is $$7$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"By using the transitive property, if $$a = b$$ and $$b = 7$$, then $$a = 7$$.<br>\r\nTherefore, the value of a is $$7$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of t, if $$m + 2 = n$$ and $$n = 3$$?\",\n                    \"text\": \"What is the value of t, if $$m + 2 = n$$ and $$n = 3$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"By using the transitive property, if $$m + 2 = n$$ and $$n=3$$, then<br>\r\n$$\\\\Rightarrow m + 2 = n$$<br>\r\n$$\\\\Rightarrow m= n$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 3$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 1$$<br>\r\nThe value of m is 1.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property, if $$m + 2 = n$$ and $$n=3$$, then<br>\r\n$$\\\\Rightarrow m + 2 = n$$<br>\r\n$$\\\\Rightarrow m= n$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 3$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 1$$<br>\r\nThe value of m is 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property, if $$m + 2 = n$$ and $$n=3$$, then<br>\r\n$$\\\\Rightarrow m + 2 = n$$<br>\r\n$$\\\\Rightarrow m= n$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 3$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 1$$<br>\r\nThe value of m is 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property, if $$m + 2 = n$$ and $$n=3$$, then<br>\r\n$$\\\\Rightarrow m + 2 = n$$<br>\r\n$$\\\\Rightarrow m= n$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 3$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 1$$<br>\r\nThe value of m is 1.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"By using the transitive property, if $$m + 2 = n$$ and $$n=3$$, then<br>\r\n$$\\\\Rightarrow m + 2 = n$$<br>\r\n$$\\\\Rightarrow m= n$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 3$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 1$$<br>\r\nThe value of m is 1.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"By using the transitive property, if $$m + 2 = n$$ and $$n=3$$, then<br>\r\n$$\\\\Rightarrow m + 2 = n$$<br>\r\n$$\\\\Rightarrow m= n$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 3$$ $$-$$ $$2$$<br>\r\n$$\\\\Rightarrow m = 1$$<br>\r\nThe value of m is 1.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of $$\\\\angle A$$, if $$\\\\angle B = \\\\angle C$$ and  $$\\\\angle C = \\\\angle A$$, and $$\\\\angle B = 45^{\\\\circ}$$.\",\n                    \"text\": \"What is the value of $$\\\\angle A$$, if $$\\\\angle B = \\\\angle C$$ and  $$\\\\angle C = \\\\angle A$$, and $$\\\\angle B = 45^{\\\\circ}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"By using the transitive property of angles,<br>\r\nIf $$\\\\angle B = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B = \\\\angle A = 45^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$60^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property of angles,<br>\r\nIf $$\\\\angle B = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B = \\\\angle A = 45^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$75^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property of angles,<br>\r\nIf $$\\\\angle B = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B = \\\\angle A = 45^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By using the transitive property of angles,<br>\r\nIf $$\\\\angle B = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B = \\\\angle A = 45^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$45^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"By using the transitive property of angles,<br>\r\nIf $$\\\\angle B = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B = \\\\angle A = 45^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"By using the transitive property of angles,<br>\r\nIf $$\\\\angle B = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B = \\\\angle A = 45^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"At what value of $$\\\\angle A$$, if $$\\\\angle B + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$, where $$\\\\angle B = 45^{\\\\circ}$$.\",\n                    \"text\": \"At what value of $$\\\\angle A$$, if $$\\\\angle B + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$, where $$\\\\angle B = 45^{\\\\circ}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If $$\\\\angle B  + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B  + 45^{\\\\circ} = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B  + 60^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$45^{\\\\circ} +  + 45^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$\\\\angle A = 90^{\\\\circ}$$<br>\r\nTherefore, the value of  $$\\\\angle A = 90^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$45^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$\\\\angle B  + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B  + 45^{\\\\circ} = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B  + 60^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$45^{\\\\circ} +  + 45^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$\\\\angle A = 90^{\\\\circ}$$<br>\r\nTherefore, the value of  $$\\\\angle A = 90^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$60^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$\\\\angle B  + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B  + 45^{\\\\circ} = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B  + 60^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$45^{\\\\circ} +  + 45^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$\\\\angle A = 90^{\\\\circ}$$<br>\r\nTherefore, the value of  $$\\\\angle A = 90^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$75^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$\\\\angle B  + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B  + 45^{\\\\circ} = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B  + 60^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$45^{\\\\circ} +  + 45^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$\\\\angle A = 90^{\\\\circ}$$<br>\r\nTherefore, the value of  $$\\\\angle A = 90^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$90^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If $$\\\\angle B  + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B  + 45^{\\\\circ} = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B  + 60^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$45^{\\\\circ} +  + 45^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$\\\\angle A = 90^{\\\\circ}$$<br>\r\nTherefore, the value of  $$\\\\angle A = 90^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If $$\\\\angle B  + 45^{\\\\circ} = \\\\angle C$$ and $$\\\\angle C = \\\\angle A$$ then automatically, $$\\\\angle B  + 45^{\\\\circ} = \\\\angle A$$.<br>\r\nTherefore, the value of  $$\\\\angle B  + 60^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$45^{\\\\circ} +  + 45^{\\\\circ} = \\\\angle A$$ <br>\r\nOr $$\\\\angle A = 90^{\\\\circ}$$<br>\r\nTherefore, the value of  $$\\\\angle A = 90^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Assume that $$3x + 3 = b$$ and $$b = 5x$$ $$-$$ 1$$. What is the value of b?\",\n                    \"text\": \"Assume that $$3x + 3 = b$$ and $$b = 5x$$ $$-$$ 1$$. What is the value of b?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In this transitive property example the solution uses the transitive property of equalities to set $$5x + 7$$ equal to $$4x$$ $$-$$ $$9$$.<br>\r\nThus, $$5x + 7 = 4x$$ $$-$$ $$9$$. Solving for x results in<br>\r\n$$5x + 7 = 4x$$ $$-$$ $$9$$<br>\r\nOr $$5x$$ $$-$$ $$4x = $$$$-$$$$9$$ $$-$$$$7$$<br>\r\nOr $$x = $$$$-$$ $$16$$<br>\r\nThe value of x is $$-16$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In this transitive property example the solution uses the transitive property of equalities to set $$5x + 7$$ equal to $$4x$$ $$-$$ $$9$$.<br>\r\nThus, $$5x + 7 = 4x$$ $$-$$ $$9$$. Solving for x results in<br>\r\n$$5x + 7 = 4x$$ $$-$$ $$9$$<br>\r\nOr $$5x$$ $$-$$ $$4x = $$$$-$$$$9$$ $$-$$$$7$$<br>\r\nOr $$x = $$$$-$$ $$16$$<br>\r\nThe value of x is $$-16$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-12$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In this transitive property example the solution uses the transitive property of equalities to set $$5x + 7$$ equal to $$4x$$ $$-$$ $$9$$.<br>\r\nThus, $$5x + 7 = 4x$$ $$-$$ $$9$$. Solving for x results in<br>\r\n$$5x + 7 = 4x$$ $$-$$ $$9$$<br>\r\nOr $$5x$$ $$-$$ $$4x = $$$$-$$$$9$$ $$-$$$$7$$<br>\r\nOr $$x = $$$$-$$ $$16$$<br>\r\nThe value of x is $$-16$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-6$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In this transitive property example the solution uses the transitive property of equalities to set $$5x + 7$$ equal to $$4x$$ $$-$$ $$9$$.<br>\r\nThus, $$5x + 7 = 4x$$ $$-$$ $$9$$. Solving for x results in<br>\r\n$$5x + 7 = 4x$$ $$-$$ $$9$$<br>\r\nOr $$5x$$ $$-$$ $$4x = $$$$-$$$$9$$ $$-$$$$7$$<br>\r\nOr $$x = $$$$-$$ $$16$$<br>\r\nThe value of x is $$-16$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-16$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In this transitive property example the solution uses the transitive property of equalities to set $$5x + 7$$ equal to $$4x$$ $$-$$ $$9$$.<br>\r\nThus, $$5x + 7 = 4x$$ $$-$$ $$9$$. Solving for x results in<br>\r\n$$5x + 7 = 4x$$ $$-$$ $$9$$<br>\r\nOr $$5x$$ $$-$$ $$4x = $$$$-$$$$9$$ $$-$$$$7$$<br>\r\nOr $$x = $$$$-$$ $$16$$<br>\r\nThe value of x is $$-16$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In this transitive property example the solution uses the transitive property of equalities to set $$5x + 7$$ equal to $$4x$$ $$-$$ $$9$$.<br>\r\nThus, $$5x + 7 = 4x$$ $$-$$ $$9$$. Solving for x results in<br>\r\n$$5x + 7 = 4x$$ $$-$$ $$9$$<br>\r\nOr $$5x$$ $$-$$ $$4x = $$$$-$$$$9$$ $$-$$$$7$$<br>\r\nOr $$x = $$$$-$$ $$16$$<br>\r\nThe value of x is $$-16$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 id=\"17-frequently-asked-questions\" class=\"wp-block-heading eplus-wrapper\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-db134b1a-3649-4fd5-ac83-118d85c2a435\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-db134b1a-3649-4fd5-ac83-118d85c2a435\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-db134b1a-3649-4fd5-ac83-118d85c2a435\"><strong>Do perpendicular lines follow transitive property?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-db134b1a-3649-4fd5-ac83-118d85c2a435\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No. If one line is perpendicular to the second line and the second line is perpendicular to the third line, then the first line becomes parallel to the third line. Thus, transitive property fails.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"561\" height=\"363\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems.png\" alt=\"Transitive property fails for perpendicular lines\" class=\"wp-image-23143\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems.png 561w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-300x194.png 300w\" sizes=\"auto, (max-width: 561px) 100vw, 561px\" \/><\/figure>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-db134b1a-3649-4fd5-ac83-118d85c2a435\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-db134b1a-3649-4fd5-ac83-118d85c2a435\"><strong>What is reflexive property?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-db134b1a-3649-4fd5-ac83-118d85c2a435\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The reflexive property states that for every real number $a$, $a = a$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-db134b1a-3649-4fd5-ac83-118d85c2a435\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-db134b1a-3649-4fd5-ac83-118d85c2a435\"><strong>What is the symmetric property?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-db134b1a-3649-4fd5-ac83-118d85c2a435\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The symmetric property states that for all real numbers a and b,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">if $a = b$ then $b = a$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-db134b1a-3649-4fd5-ac83-118d85c2a435\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-db134b1a-3649-4fd5-ac83-118d85c2a435\"><strong>What is the substitution property?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-db134b1a-3649-4fd5-ac83-118d85c2a435\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If $a = b$, then a may be replaced by b in any equation or expression.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-db134b1a-3649-4fd5-ac83-118d85c2a435\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-db134b1a-3649-4fd5-ac83-118d85c2a435\"><strong>Where do we use the transitive property?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-db134b1a-3649-4fd5-ac83-118d85c2a435\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The transitive property is generally used, when we have multiple quantities, which have the same category and are related by the same rule.<\/p>\n\n<\/div><\/div>\n<\/div>\n\n\n<h2 id=\"18-related-articles\" class=\"wp-block-heading eplus-wrapper\">Related Articles<\/h2>\n\n\n\n<ul class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-properties\">Number Properties<\/a><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication\">Properties of Multiplication<\/a><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/commutative-property\">Commutative Property<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Transitive Property: Introduction Transitive property refers to a property by which if number a is related to the number b by a certain rule, and the number b is related to the number c by the same rule, then we can definitely say that the number a is related to the number c by the &#8230; <a title=\"Transitive Property\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/transitive-property\" aria-label=\"More on Transitive Property\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-23130","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23130","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=23130"}],"version-history":[{"count":14,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23130\/revisions"}],"predecessor-version":[{"id":42304,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23130\/revisions\/42304"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=23130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=23130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=23130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}