{"id":32060,"date":"2023-07-21T18:56:00","date_gmt":"2023-07-21T18:56:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=32060"},"modified":"2023-07-23T04:48:39","modified_gmt":"2023-07-23T04:48:39","slug":"midsegment-of-a-triangle-definition-theorem-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/midsegment-of-a-triangle","title":{"rendered":"Midsegment of a Triangle: Definition, Theorem, Formula, Examples"},"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-251f73a8-6cc7-4249-826d-f50fe4af3c48\" 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\/midsegment-of-a-triangle#0-what-is-the-midsegment-of-a-triangle>What Is the Midsegment of a Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/midsegment-of-a-triangle#4-proof-of-midsegment-theorem-of-a-triangle>Proof of Midsegment Theorem of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/midsegment-of-a-triangle#8-midsegment-formula>Midsegment Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/midsegment-of-a-triangle#11-solved-examples-on-midsegment-of-a-triangle>Solved Examples on Midsegment of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/midsegment-of-a-triangle#12-practice-problems-on-midsegment-of-a-triangle>Practice Problems on Midsegment of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/midsegment-of-a-triangle#13-frequently-asked-questions-about-midsegment-of-a-triangle>Frequently Asked Questions about Midsegment of a Triangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-midsegment-of-a-triangle\">What Is the Midsegment of a Triangle?<\/h2>\n\n\n\n<p><strong>The midsegment of a triangle is a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/line-segment\"><strong>line segment<\/strong><\/a><strong> joining the midpoints of two sides of the triangle. A triangle has three midsegments.<\/strong><\/p>\n\n\n\n<p>Consider the triangle PQR in the given diagram. The points P, Q, and R are the three vertices of the triangle. PQ, QR, and PR are the three sides. Point A is the midpoint of side PR. Point B is the midpoint of side PQ.&nbsp;<\/p>\n\n\n\n<p>The line segment AB that joins the midpoints A and B. It is the midsegment of the triangle PQR.<\/p>\n\n\n\n<p>Notice that AB is parallel to the side QR.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"366\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment.png\" alt=\"Midsegment of a triangle\" class=\"wp-image-32067\" title=\"Midsegment of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-300x177.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Midpoint is the middle or center point of a line segment that divides it into two equal parts. It is equidistant from both <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/endpoint\">endpoints<\/a> of a line segment. A triangle is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">polygon<\/a> with 3 sides, 3 <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometry\">angles<\/a>, and 3 vertices.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"285\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midpoint.png\" alt=\"B as a midpoint of line segment AC.\" class=\"wp-image-32069\" title=\"B as a midpoint of line segment AC.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midpoint.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midpoint-300x138.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\/answer-questions-related-to-triangles\" 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\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles 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\">Answer Questions Related to Triangles 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\/classify-triangles-and-rectangles-as-closed-shape\" 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\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape 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\">Classify Triangles and Rectangles as Closed Shape 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\/classify-triangles\" 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\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles 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\">Classify Triangles 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\/identify-the-type-of-triangles-based-on-angles\" 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\/geometry_classify_tri_on_angle_pt.png\" alt=\"Identify the Type of Triangles Based on Angles 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\">Identify the Type of Triangles Based on Angles 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\/identify-triangles-and-rectangles\" 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\/geometry_amusement_park_18_20_gm.png\" alt=\"Identify Triangles and Rectangles 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\">Identify Triangles and Rectangles 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\/identify-triangles-and-squares\" 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\/geometry_triangles_squares_pt.png\" alt=\"Identify Triangles and Squares 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\">Identify Triangles and Squares 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\/identify-types-of-triangles\" 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\/geometry_types_of_triangles_pt.png\" alt=\"Identify Types of Triangles 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\">Identify Types of Triangles 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\/match-triangles-and-squares\" 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\/geometry_amusement_park_4_5_gm.png\" alt=\"Match Triangles and Squares 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\">Match Triangles and Squares 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\/triangles-and-rectangles\" 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\/geometry_triangle_rectangle_1_pt.png\" alt=\"Triangles and Rectangles 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\">Triangles and Rectangles 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                    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to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-midsegment-of-a-triangle-definition\">Midsegment of a Triangle: Definition<\/h2>\n\n\n\n<p>The midsegment is a line segment that joins the midpoints of any two sides of a triangle.&nbsp;<\/p>\n\n\n\n<p>So, how many midsegments does a triangle have? The answer is 3.<\/p>\n\n\n\n<p>In the triangle ABC shown below, the three midsegments are XY, YZ, and XZ.<\/p>\n\n\n\n<p>Here,&nbsp;<\/p>\n\n\n\n<p>AB || XY<\/p>\n\n\n\n<p>AC || YZ<\/p>\n\n\n\n<p>BC || XZ<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"347\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-a-triangle.png\" alt=\"Three midsegments of a triangle ABC\" class=\"wp-image-32070\" title=\"Three midsegments of a triangle ABC\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-a-triangle-300x168.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\/rectangles-and-triangles\" 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\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles 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\/separate-out-the-triangles\" 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\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles 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 class=\"wp-block-heading\" id=\"2-properties-of-the-midsegment\">Properties of the Midsegment<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"325\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-triangle-ABC.png\" alt=\"Midsegments FE, EF, DF of a triangle ABC\" class=\"wp-image-32071\" title=\"Midsegments FE, EF, DF of a triangle ABC\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-triangle-ABC.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-triangle-ABC-300x157.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A triangle has three midsegments.&nbsp;<\/strong><\/li>\n<\/ul>\n\n\n\n<p>DE, EF, DF are three midsegments of the triangle ABC.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A midsegment joins the midpoints of two sides.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>D is the midpoint of the side AB.<\/p>\n\n\n\n<p>E is the midpoint of the side AC.<\/p>\n\n\n\n<p>F is the midpoint of the side BC.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>The midsegment of a triangle is always parallel to the third side of the triangle.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>DE || BC<\/p>\n\n\n\n<p>EF || AB<\/p>\n\n\n\n<p>DF || AC<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>The length of the midsegment is half the length of the third side.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>DE $= \\frac{1}{2}$ BC<\/p>\n\n\n\n<p>EF $= \\frac{1}{2}$ AB<\/p>\n\n\n\n<p>DF $= \\frac{1}{2}$ AC<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>The three midsegments of a triangle form a triangle similar to the original triangle.&nbsp;<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong><strong>DEF <\/strong><strong><\/strong><strong>&nbsp; <\/strong><strong>ABC<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>The smaller triangle formed by the midsegments is <\/strong>$\\frac{1}{4}$<strong>th area of the original triangle and half the perimeter of the original triangle.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Area of $\\Delta \\text{BDF} = \\text{Area of} \\Delta \\text{CEF} = \\text{Area of} \\Delta ADE = \\frac{1}{4} \\times \\Delta \\text{ABC}$<\/p>\n\n\n\n<p>Perimeter of $\\Delta \\text{BDF} = \\text{Perimeter of} \\Delta \\text{CEF} = \\text{Perimeter of} \\Delta \\text{ADE} = \\frac{1}{2} \\times \\text{Perimeter of} \\Delta \\text{ABC}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-midsegment-theorem-of-a-triangle\">Midsegment Theorem of a Triangle<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-d9fb2019-7ab2-494d-8c11-fa1e3800a663\">\n\n\n<p><strong>Triangle Midsegment Theorem Statement:<\/strong> The line segment joining the midpoints or centers of any two sides of a triangle is parallel to the third side and half of it in length.<\/p>\n\n\n<\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"361\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-triangle-PQR.png\" alt=\"Midsegment of a triangle theorem\" class=\"wp-image-32072\" title=\"Midsegment of a triangle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-triangle-PQR.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-triangle-PQR-300x175.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>According to the midsegment theorem:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AB || RQ, AB $= \\frac{1}{2}$ RQ<\/li>\n\n\n\n<li>AC || PQ, AC$= \\frac{1}{2}$ PQ<\/li>\n\n\n\n<li>BC || PR, BC$= \\frac{1}{2}$ PR<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-proof-of-midsegment-theorem-of-a-triangle\">Proof of Midsegment Theorem of a Triangle<\/h2>\n\n\n\n<p><strong>To prove:<\/strong>&nbsp;<\/p>\n\n\n\n<p>In the triangle PQR,<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AB || RQ<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AB $= \\frac{1}{2}$ RQ<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/triangle-pqr-midsegment-ab.png\" alt=\"Midsegment AB of a triangle PQR\" class=\"wp-image-32073\" title=\"Midsegment AB of a triangle PQR\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/triangle-pqr-midsegment-ab.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/triangle-pqr-midsegment-ab-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Construction:<\/strong> Extend the line AB from the point B. Construct a line QC parallel to AR, such that it meets the extended line AB at point C.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-theorem-construction.png\" alt=\"Construction for proof of midsegment of a triangle theorem\" class=\"wp-image-32074\" title=\"Construction for proof of midsegment of a triangle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-theorem-construction.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-theorem-construction-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>A is the midpoint of PR. B is the midpoint of PQ.<\/p>\n\n\n\n<p>In $\\Delta PAB$ and $\\Delta QCB$<\/p>\n\n\n\n<p>$PB = BQ$                               $\\therefore$ B is the midpoint of PQ\u00a0<\/p>\n\n\n\n<p>$\\angle APB\u00a0 = \\angle CQB$                    $\\therefore$ Alternate angles<\/p>\n\n\n\n<p>$\\angle ABP\u00a0 = \\angle CBQ$                  $\\therefore$ Vertically Opposite angles<\/p>\n\n\n\n<p>Therefore, by AAS congruence criteria of a triangle, we have<\/p>\n\n\n\n<p>$\\Delta ADE \\cong \\Delta CFE$.<\/p>\n\n\n\n<p>By CPCTC (Corresponding Parts of Congruent Triangles are Congruent),&nbsp;<\/p>\n\n\n\n<p>$PA = QC$ and $AB = BC$ \u2026(1)<\/p>\n\n\n\n<p>Now, we have<\/p>\n\n\n\n<p>$PA = AR$ A is the midpoint of PR. \u2026(2)<\/p>\n\n\n\n<p>$PA = QC$ from (1) \u2026(3)<\/p>\n\n\n\n<p>We can say that&nbsp;<\/p>\n\n\n\n<p>$PA = AR = CQ$ \u00a0 \u2026from (1),(2),(3)<\/p>\n\n\n\n<p>As AC || RQ, AR || CQ, and AR = CQ, we can say that ACQR is a parallelogram.&nbsp;<\/p>\n\n\n\n<p>Therefore, AC = RQ.&nbsp;<\/p>\n\n\n\n<p>Here, $AB = \\frac{1}{2}$ AC and AC = RQ<\/p>\n\n\n\n<p>Hence, $AB = \\frac{1}{2}$ RQ<\/p>\n\n\n\n<p>Also, as ACRQ, we have ABRQ&nbsp;<\/p>\n\n\n\n<p>Hence proved.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-converse-of-midsegment-theorem-of-a-triangle\">Converse of Midsegment Theorem of a Triangle<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-f8457e6c-5b7c-4b78-a92c-9d5e192d9ab2\">\n\n\n<p><strong>Converse of the midsegment theorem<\/strong>: If a line segment joining any two sides of a triangle is parallel to the third side and is half the length of the third side, then it is the midsegment of the triangle.<\/p>\n\n\n<\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-of-a-triangle-image.png\" alt=\"Converse of Midsegment of a triangle theorem\" class=\"wp-image-32075\" title=\"Converse of Midsegment of a triangle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-of-a-triangle-image.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-of-a-triangle-image-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>In $\\Delta PQR$, if A is the midpoint of sides PR, AB || RQ and\u00a0 $AB = \\frac{1}{2}\\; RQ$, then AB is the midsegment of the $\\Delta PQR$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-proof-of-converse-of-midsegment-theorem\">Proof of Converse of Midsegment Theorem<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"307\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-visual.png\" alt=\"Proof of Converse of Midsegment of a triangle theorem\" class=\"wp-image-32076\" title=\"Proof of Converse of Midsegment of a triangle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-visual.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-visual-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Given:<\/strong> In triangle PQR, AB joins two sides PR and PQ of a triangle PQR.<\/p>\n\n\n\n<p>AB || QR<\/p>\n\n\n\n<p>$AB = \\frac{1}{2} \\times QR$<\/p>\n\n\n\n<p><strong>To prove:<\/strong> AB is the midsegment of $\\Delta PQR$.<\/p>\n\n\n\n<p>OR&nbsp;<\/p>\n\n\n\n<p>B is the midpoint of PQ and A is the midpoint of PR.<\/p>\n\n\n\n<p><strong>Construction:<\/strong> Extend the line AB from the point B to the point C, such that $AB = BC$.<\/p>\n\n\n\n<p>Construct a line QC parallel to AR, such that both lines meet at point C.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"450\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/construction-for-midsgement-theorem-proof.png\" alt=\"Construction for Proof of Converse of Midsegment of a triangle theorem\" class=\"wp-image-32077\" title=\"Construction for Proof of Converse of Midsegment of a triangle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/construction-for-midsgement-theorem-proof.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/construction-for-midsgement-theorem-proof-300x218.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>It is given that A is the midpoint of PR, AB || RQ and\u00a0 AB $= \\frac{1}{2}$ RQ.<\/p>\n\n\n\n<p>$AB = BC$ \u2026construction<\/p>\n\n\n\n<p>$AB = \\frac{1}{2} RQ$ \u2026Given<\/p>\n\n\n\n<p>Thus, $AC = QR$<\/p>\n\n\n\n<p>Also, AR || CQ \u2026Given<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0AB || RQ \u2026Construction<\/p>\n\n\n\n<p>Therefore, DBCF is a parallelogram.<\/p>\n\n\n\n<p>We know that opposite sides of a parallelogram are parallel and equal.<\/p>\n\n\n\n<p>Therefore, $AR = CQ$ and PA || CQ \u2026(1)<\/p>\n\n\n\n<p>In $\\Delta PAB$ and $\\Delta QBC$,<\/p>\n\n\n\n<p>$\\angle APB\u00a0 = \\angle CQB$ (Alternate angles)\u00a0<\/p>\n\n\n\n<p>$AB = BC$\u00a0 \u00a0\u00a0<\/p>\n\n\n\n<p>$\\angle PBA\u00a0 = \\angle QBC$ (Vertically opposite angle)\u00a0\u00a0<\/p>\n\n\n\n<p>So, by AAS congruence criterion, $\\Delta PAB \\cong \\Delta QBC$<\/p>\n\n\n\n<p>Using CPCTC, we write<\/p>\n\n\n\n<p>$PB = BQ$<\/p>\n\n\n\n<p>$CQ = AP$<\/p>\n\n\n\n<p>But $AR = CQ$\u00a0 \u2026from (1)<\/p>\n\n\n\n<p>Thus, $AP = AR$<\/p>\n\n\n\n<p>Therefore, AB is the midsegment of $\\Delta PQR$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-how-to-find-the-midsegment-of-a-triangle\">How to Find the Midsegment of a Triangle<\/h2>\n\n\n\n<p>To construct the midsegment of a triangle, we find midpoints of any two sides of the triangle.<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Put the compass on the vertex B. Keep the compass distance more than half the length of BC. Draw arcs on both sides of BC. Draw similar arcs keeping the compass on the vertex C to intersect the previous arcs at points D and G respectively. Draw a line joining the points D and G. Let the line DG intersect the side BC at the point T. T is the midpoint of the side BC.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Similarly, find the midpoint of the side AB. Let S be the midpoint of side AB.<\/p>\n\n\n\n<p><strong>Step 3<\/strong>: Join S and T. The segment joining S and T is the midsegment of the triangle ABC.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"400\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-construction.png\" alt=\"Construction of midsegment of a triangle\" class=\"wp-image-32078\" title=\"Construction of midsegment of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-construction.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-construction-300x194.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-midsegment-formula\">Midsegment Formula<\/h2>\n\n\n\n<p>The formula to find the length of the midsegment is<\/p>\n\n\n\n<p>Length of the midsegment $= \\frac{1}{2} \\times$ Length of the base of triangle<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-facts-about-the-midsegment-of-a-triangle\">Facts about the Midsegment of a Triangle<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.<\/li>\n\n\n\n<li>The midsegment of a triangle theorem is also known as the mid-point theorem.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the midsegment of a triangle. It is the line that joins the midpoints or center of any two sides of a triangle. Let\u2019s solve a few examples of the midsegment of a triangle for a better understanding!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-solved-examples-on-midsegment-of-a-triangle\">Solved Examples on Midsegment of a Triangle<\/h2>\n\n\n\n<p><strong>1. Find the value of <\/strong><strong><em>x <\/em><\/strong><strong>if MN is the midsegment of the triangle XYZ.&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"255\" height=\"232\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-problem.png\" alt=\"Applying the midsegment theorem example\" class=\"wp-image-32079\" title=\"Applying the midsegment theorem example\"\/><\/figure>\n\n\n\n<p><strong>Solution: <\/strong>&nbsp;According to the midsegment theorem, the length of the midsegment is half the length of the third side.<\/p>\n\n\n\n<p>$MN = \\frac{1}{2} \\times QR$<\/p>\n\n\n\n<p>QR $= 2$ MN\u00a0<\/p>\n\n\n\n<p>$10x = 2 \\times 35$<\/p>\n\n\n\n<p>$10x = 70$<\/p>\n\n\n\n<p>$x = 7$ units<\/p>\n\n\n\n<p><strong>2. In the triangle below it is given that BC <\/strong>$= 36$<strong>cm, and M, N are the midpoints of AB and AC. Find XY.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"255\" height=\"232\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-midsegment-length-example.png\" alt=\"Question on midsegment of a triangle\" class=\"wp-image-32080\" title=\"Question on midsegment of a triangle\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong> According to the midsegment theorem, the length of the midsegment is half the length of the third side.<\/p>\n\n\n\n<p>$XY = \\frac{1}{2}\\; BC$<\/p>\n\n\n\n<p>$XY = \\frac{1}{2} \\times 36$<\/p>\n\n\n\n<p>$XY = 18$ in<\/p>\n\n\n\n<p><strong>3. AB is the midsegment of the triangle ABC. Find the value of x.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"255\" height=\"232\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-solved-example.png\" alt=\"Midsegment of triangle XYZ with length (3x-1)\" class=\"wp-image-32081\" title=\"Midsegment of triangle XYZ with length (3x-1)\"\/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>According to the midsegment theorem, the length of the midsegment is half the length of the third side.<\/p>\n\n\n\n<p>$AB = \\frac{1}{2} \\times XZ$<\/p>\n\n\n\n<p>$3x \\;-\\; 1 = \\frac{1}{2} \\times 34$<\/p>\n\n\n\n<p>$3x \\;-\\; 1 = 17$<\/p>\n\n\n\n<p>$3x = 18$<\/p>\n\n\n\n<p>$x = 6$ feet<\/p>\n\n\n\n<p><strong>4. If ABC is an equilateral triangle with a midsegment of length 12 units then find the perimeter of the triangle ABC.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>According to the midsegment theorem,<\/p>\n\n\n\n<p>Length of the midsegment $= \\frac{1}{2} \\times$ length of the base of triangle<\/p>\n\n\n\n<p>Let the side of the equilateral triangle be x<em>.<\/em><\/p>\n\n\n\n<p>$12 = \\frac{1}{2} \\times x$<\/p>\n\n\n\n<p>$x = 2 \\times 12$<\/p>\n\n\n\n<p>$x = 24$ units<\/p>\n\n\n\n<p>Perimeter of an equilateral triangle $= 4x = 4 \\times 24 = 96$ units<\/p>\n\n\n\n<p><strong>5. Find the perimeter of <\/strong>$\\Delta DEF$<strong>, if the perimeter of <\/strong>$\\Delta ABC$<strong> is 72 units.\u00a0<\/strong><\/p>\n\n\n\n<p><strong>DE, EF, and DF are midsegments.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"257\" height=\"234\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegments-of-trianlge.png\" alt=\"\u0394DEF inside \u0394ABC\" class=\"wp-image-32082\" title=\"\u0394DEF inside \u0394ABC\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>By the midsegment theorem, we have<\/p>\n\n\n\n<p>DE || BC and DE $= \\frac{1}{2}\\times$ BC \u2003\u2014\u2014\u2014\u2014\u2014\u2014 (i)<\/p>\n\n\n\n<p>Similarly,&nbsp;<\/p>\n\n\n\n<p>DF || AC and DF $= \\frac{1}{2}\\times$ AC \u2003\u2014\u2014\u2014\u2014\u2014\u2014 (ii)<\/p>\n\n\n\n<p>and&nbsp;<\/p>\n\n\n\n<p>EF || AB and EF $= \\frac{1}{2} \\times$ AB \u2003\u2014\u2014\u2014\u2014\u2014\u2014 (iii)<\/p>\n\n\n\n<p>Now, the perimeter of $\\Delta DEF = DE + EF + FD$<\/p>\n\n\n\n<p>$\\Rightarrow$ Perimeter of $\\Delta DEF = \\frac{1}{2} BC + \\frac{1}{2} AC + \\frac{1}{2} AB$ \u2003(from equation i, ii and iii)<\/p>\n\n\n\n<p>$\\Rightarrow$ Perimeter of $\\Delta DEF = \\frac{1}{2} (BC + AC + AB)$<\/p>\n\n\n\n<p>$\\Rightarrow$ Perimeter of $\\Delta DEF = \\frac{1}{2}$ $(\\text{Perimeter of} \\Delta ABC) = \\frac{1}{2} \\times 72 = 36$ cm.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-practice-problems-on-midsegment-of-a-triangle\">Practice Problems on Midsegment of a Triangle<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Midsegment of a Triangle: Definition, Theorem, Formula, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">In the triangle LMN, if OP is the midsegment, which of the following statements is true?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-example.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$OP = MN$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$OP = 2MN$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2OP = MN$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$OP = 3MN$<\/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: $2OP = MN$<br\/>According to the midsegment theorem, the length of the midsegment is half the length of the third side.<br>\r\n$2OP = MN$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The triangle formed by joining the midsegments of an equilateral triangle is _____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">a right angle triangle<\/div><div class=\"spq_answer_block\" data-value=\"1\">a parallelogram<\/div><div class=\"spq_answer_block\" data-value=\"2\">an isosceles triangle<\/div><div class=\"spq_answer_block\" data-value=\"3\">an equilateral triangle<\/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: an equilateral triangle<br\/>The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.<\/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\">If ABC is an equilateral triangle with a perimeter of 45 units. Find the length of its midsegment.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">7.5 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">90 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">15 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">30 units<\/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: 7.5 units<br\/>Perimeter of an equilateral triangle $= 3\\times$ side<br>\r\n$45 = 3 \\times$ side<br>\r\nThus, side $= 15$<br>\r\nLength of the midsegment $= \\frac{1}{2}\\times$ length of the base of triangle<br>\r\nMidsegmen $= \\frac{1}{2} \\times 15 = 7.5$ units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">A triangle has ______ midsegments.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4<\/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\">6<\/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: 3<br\/>A triangle has 3 midsegments.<\/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\": \"Midsegment of a Triangle: Definition, Theorem, Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Midsegment of a Triangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In the triangle LMN, if OP is the midsegment, which of the following statements is true?\",\n                    \"text\": \"In the triangle LMN, if OP is the midsegment, which of the following statements is true? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/midsegment-example.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the midsegment theorem, the length of the midsegment is half the length of the third side.<br>\r\n$$2OP = MN$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$OP = MN$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the midsegment theorem, the length of the midsegment is half the length of the third side.<br>\r\n$$2OP = MN$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$OP = 2MN$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the midsegment theorem, the length of the midsegment is half the length of the third side.<br>\r\n$$2OP = MN$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$OP = 3MN$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the midsegment theorem, the length of the midsegment is half the length of the third side.<br>\r\n$$2OP = MN$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$2OP = MN$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the midsegment theorem, the length of the midsegment is half the length of the third side.<br>\r\n$$2OP = MN$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the midsegment theorem, the length of the midsegment is half the length of the third side.<br>\r\n$$2OP = MN$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The triangle formed by joining the midsegments of an equilateral triangle is _____.\",\n                    \"text\": \"The triangle formed by joining the midsegments of an equilateral triangle is _____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a right angle triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a parallelogram\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"an isosceles triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"an equilateral triangle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The triangle formed by joining the midsegments of an equilateral triangle is an equilateral triangle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If ABC is an equilateral triangle with a perimeter of 45 units. Find the length of its midsegment.\",\n                    \"text\": \"If ABC is an equilateral triangle with a perimeter of 45 units. Find the length of its midsegment.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Perimeter of an equilateral triangle $$= 3\\\\times$$ side<br>\r\n$$45 = 3 \\\\times$$ side<br>\r\nThus, side $$= 15$$<br>\r\nLength of the midsegment $$= \\\\frac{1}{2}\\\\times$$ length of the base of triangle<br>\r\nMidsegmen $$= \\\\frac{1}{2} \\\\times 15 = 7.5$$ units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"90 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of an equilateral triangle $$= 3\\\\times$$ side<br>\r\n$$45 = 3 \\\\times$$ side<br>\r\nThus, side $$= 15$$<br>\r\nLength of the midsegment $$= \\\\frac{1}{2}\\\\times$$ length of the base of triangle<br>\r\nMidsegmen $$= \\\\frac{1}{2} \\\\times 15 = 7.5$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of an equilateral triangle $$= 3\\\\times$$ side<br>\r\n$$45 = 3 \\\\times$$ side<br>\r\nThus, side $$= 15$$<br>\r\nLength of the midsegment $$= \\\\frac{1}{2}\\\\times$$ length of the base of triangle<br>\r\nMidsegmen $$= \\\\frac{1}{2} \\\\times 15 = 7.5$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of an equilateral triangle $$= 3\\\\times$$ side<br>\r\n$$45 = 3 \\\\times$$ side<br>\r\nThus, side $$= 15$$<br>\r\nLength of the midsegment $$= \\\\frac{1}{2}\\\\times$$ length of the base of triangle<br>\r\nMidsegmen $$= \\\\frac{1}{2} \\\\times 15 = 7.5$$ units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"7.5 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Perimeter of an equilateral triangle $$= 3\\\\times$$ side<br>\r\n$$45 = 3 \\\\times$$ side<br>\r\nThus, side $$= 15$$<br>\r\nLength of the midsegment $$= \\\\frac{1}{2}\\\\times$$ length of the base of triangle<br>\r\nMidsegmen $$= \\\\frac{1}{2} \\\\times 15 = 7.5$$ units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Perimeter of an equilateral triangle $$= 3\\\\times$$ side<br>\r\n$$45 = 3 \\\\times$$ side<br>\r\nThus, side $$= 15$$<br>\r\nLength of the midsegment $$= \\\\frac{1}{2}\\\\times$$ length of the base of triangle<br>\r\nMidsegmen $$= \\\\frac{1}{2} \\\\times 15 = 7.5$$ units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A triangle has ______ midsegments.\",\n                    \"text\": \"A triangle has ______ midsegments.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A triangle has 3 midsegments.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangle has 3 midsegments.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangle has 3 midsegments.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangle has 3 midsegments.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"3\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A triangle has 3 midsegments.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A triangle has 3 midsegments.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-frequently-asked-questions-about-midsegment-of-a-triangle\">Frequently Asked Questions about Midsegment of a Triangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7ba35849-301f-40e1-924a-edbf668e904b\" 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-0-7ba35849-301f-40e1-924a-edbf668e904b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7ba35849-301f-40e1-924a-edbf668e904b\"><strong>How many midsegments does a triangle have?<\/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-0-7ba35849-301f-40e1-924a-edbf668e904b\">\n\n<p>A triangle has three midsegments.<\/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-1-7ba35849-301f-40e1-924a-edbf668e904b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7ba35849-301f-40e1-924a-edbf668e904b\"><strong>How many midsegments does a triangle have?<\/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-1-7ba35849-301f-40e1-924a-edbf668e904b\">\n\n<p>The formula to find the length of the midsegment is<\/p>\n\n\n\n<p>Length of the midsegment $= \\frac{1}{2} \\times$ Length of the base of triangle<\/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-2-7ba35849-301f-40e1-924a-edbf668e904b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7ba35849-301f-40e1-924a-edbf668e904b\"><strong><strong>Are all the midsegments of a triangle equal in length?<\/strong><\/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-2-7ba35849-301f-40e1-924a-edbf668e904b\">\n\n<p>All the midsegments of a triangle are equal in length only in the case of an equilateral triangle. In an <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/isosceles-triangle\">isosceles triangle<\/a>, two midsegments are equal in length whereas, in a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/scalene-triangle\">scalene triangle<\/a>, no midsegments are equal.<\/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-3-7ba35849-301f-40e1-924a-edbf668e904b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7ba35849-301f-40e1-924a-edbf668e904b\"><strong>What are some applications of the midsegment theorem of a triangle and its converse?<\/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-3-7ba35849-301f-40e1-924a-edbf668e904b\">\n\n<p>The midsegment in <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometry\">geometry<\/a> is a concept that can be used to find missing side lengths in triangles, to determine if a triangle is isosceles, and to find the center of a triangle. It can also be used in engineering and architecture to design structures with specific properties.<\/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-4-7ba35849-301f-40e1-924a-edbf668e904b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7ba35849-301f-40e1-924a-edbf668e904b\"><strong>How long is the midsegment of a triangle?<\/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-4-7ba35849-301f-40e1-924a-edbf668e904b\">\n\n<p>The midsegment of a triangle is half the length of the third side.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Midsegment of a Triangle? The midsegment of a triangle is a line segment joining the midpoints of two sides of the triangle. A triangle has three midsegments. Consider the triangle PQR in the given diagram. The points P, Q, and R are the three vertices of the triangle. PQ, QR, and PR &#8230; <a title=\"Midsegment of a Triangle: Definition, Theorem, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/midsegment-of-a-triangle\" aria-label=\"More on Midsegment of a Triangle: Definition, Theorem, Formula, Examples\">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-32060","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\/32060","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=32060"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32060\/revisions"}],"predecessor-version":[{"id":32089,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32060\/revisions\/32089"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}