{"id":25576,"date":"2023-02-28T05:21:10","date_gmt":"2023-02-28T05:21:10","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=25576"},"modified":"2024-02-05T15:25:06","modified_gmt":"2024-02-05T15:25:06","slug":"median-of-triangle-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/median-of-a-triangle","title":{"rendered":"Median of Triangle: Definition with 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-959c433a-1914-4190-89fd-772c33aa1a58\" 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\/median-of-a-triangle#0-what-is-the-median-of-a-triangle>What Is the Median of a Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/median-of-a-triangle#2-properties-of-median-of-triangle>Properties of Median of Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/median-of-a-triangle#3-difference-between-altitude-and-median-of-a-triangle>Difference between Altitude and Median of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/median-of-a-triangle#10-solved-examples-on-median-of-a-triangle>Solved Examples On Median of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/median-of-a-triangle#11-practice-problems-on-median-of-a-triangle>Practice Problems On Median of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/median-of-a-triangle#12-frequently-asked-questions-on-median-of-a-triangle>Frequently Asked Questions On Median of a Triangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-median-of-a-triangle\">What Is the Median of a Triangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Triangle is a closed figure with three sides, three interior angles, and three vertices. <strong>A median of a triangle is a line segment that joins a vertex to the midpoint of the side that is opposite to that vertex.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"411\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle.png\" alt=\"Median of a triangle\" class=\"wp-image-36895\" title=\"Median of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-300x199.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the above figure, A, B, and C are vertices of the triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">D is the midpoint of the line segment BC.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The line AB is a median of the triangle ABC.<\/p>\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                    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 eplus-wrapper\" id=\"1-definition-of-median-of-a-triangle\">Definition of Median of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>A median of a triangle can be defined as a line segment drawn from a vertex of a triangle that bisects the opposite side of a triangle.<\/strong><\/p>\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 eplus-wrapper\" id=\"2-properties-of-median-of-triangle\">Properties of Median of Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s discuss some important properties of the median of triangles.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">It bisects the opposite side into two equal parts.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Every triangle has three medians, one from each vertex to its opposite side.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">No matter what the shape of the triangle is, the three medians always meet at a single point.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The points where the three medians meet are called the centroid of the triangle.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The median of a triangle divides the triangle into two triangles having equal area.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The three medians of a triangle divide the triangle into six smaller triangles of equal area.&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"407\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/medians-and-the-centroid-of-a-triangle.png\" alt=\"Medians and the centroid of a triangle\" class=\"wp-image-36897\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/medians-and-the-centroid-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/medians-and-the-centroid-of-a-triangle-300x197.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-difference-between-altitude-and-median-of-a-triangle\">Difference between Altitude and Median of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In any triangle, the median and altitude are not the same. An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at a right angle. It is the shortest distance between the vertex and the line opposite to that vertex. Whereas, a median is a line segment that connects a vertex to the midpoint point of the opposite side.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"442\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/altitude-and-median-of-a-triangle.png\" alt=\"Altitude and median of a triangle\" class=\"wp-image-36898\" title=\"Altitude and median of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/altitude-and-median-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/altitude-and-median-of-a-triangle-300x214.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-find-the-median-of-a-triangle\">How to Find the Median of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The length of the median of a triangle can be determined using the basic formula, which can be derived from Apollonius\u2019s Theorem.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-apolloniuss-theorem-to-find-median-of-a-triangle\">Apollonius&#8217;s Theorem to Find Median of a Triangle<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It states that in any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median that bisects the third side.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The above-mentioned theorem is a bit wordy but can be transformed into a formula that gives the median of the triangle formula.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-median-of-triangle-formula\">Median of Triangle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us consider a, b, and c are the lengths of the sides of a triangle, and $\\text{m}_{a},\\; \\text{m}_{b},$ and $m_{c}$ are the medians formed on side a, side b, and side c respectively.<\/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\/median-of-a-triangle-formula.png\" alt=\"Median of a triangle formula\" class=\"wp-image-36899\" title=\"Median of a triangle formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-formula-300x186.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The first median of a triangle $(m_{a})$ drawn on the side \u201ca\u201d can be calculated using the formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m^{a}=\\sqrt{\\frac{2b^2 +2c^2\\;-\\;a^2}{4}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, the second median of a triangle $(m_{b})$ drawn on the side \u201cb\u201d can be calculated using the formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m_{b} = \\sqrt{\\frac{2a^2 +2c^2\\;-\\;b^2}{4}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, the third median of a triangle $(m_{c})$ drawn on the side \u201cc\u201d can be calculated using the formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m_{c} = \\sqrt{\\frac{2a^2 +2b^2\\;-\\;c^2}{4}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-how-to-find-the-median-of-the-triangle-using-coordinates-of-vertices\">How to find the Median of the Triangle Using Coordinates of Vertices<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When we have the coordinates of the three vertices of a triangle, we can find out the length of the median of the triangle by following the steps given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"516\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-using-coordinates.png\" alt=\"Median of a triangle using coordinates\" class=\"wp-image-36900\" title=\"Median of a triangle using coordinates\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-using-coordinates.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-using-coordinates-300x250.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Using the midpoint formula, find the midpoint of BC, which points D. Let the coordinates of point D be $(a_{1},\\; b_{1})$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In geometry, the midpoint is the middle point of a line segment. For any two points $(x_{1},\\; y_{1})$ and $(x_{2}, y_{2})$ midpoint is given by&nbsp; $\\bigg(\\frac{x_{1} + x_{2}}{2},\\; \\frac{y_{1} + y_{2}}{2}\\bigg)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here for point D, the midpoint is calculated as,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">D$(a_{1},\\;b_{1}) = \\bigg(\\frac{x_{2} + x_{3}}{2},\\; \\frac{y_{2} + y_{3}}{2}\\bigg)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Find the length of median AD using the distance formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In geometry, the distance formula is used to find the length or distance between two points when their coordinates are given. For any two points $(x_{1},\\; y_{1})$ and $(x_{2},\\; y_{2})$ distance formula is given by $\\sqrt{(x_{2}\\;-\\;x_{1})^{2} + (y_{2}\\;-\\;y_{1})^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the length of median AD $ = \\sqrt{(a_{1}\\;-\\;x_{1})2 + (b_{1}\\;-\\;y_{1})^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, we can find the lengths of median BE and CF.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The points where the medians of a triangle meet are known as the centroid. It is also called the center of gravity of the triangle.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The median of a triangle divides the triangle into two triangles having equal area.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The three medians of a triangle divide the triangle into six smaller triangles of equal area.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The sum of the length of three medians of a triangle is greater than its perimeter.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The medians of congruent triangles are equal because the corresponding parts of congruent triangles are congruent.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">In a scalene triangle, the medians have different lengths.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">In an equilateral triangle, the length of the medians is the same.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The altitude of a triangle may lie inside or outside the triangle<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The centroid of a triangle divides each median in the ratio 2:1.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about the median and altitude of a triangle, properties of the median of a triangle, and different methods to find the median of a triangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples-on-median-of-a-triangle\">Solved Examples On Median of a Triangle<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>In the figure given below identify the medians of the triangle. What is their point of intersection called?<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"264\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-and-centroid-example.png\" alt=\"Median of a triangle and centroid example\" class=\"wp-image-36901\" title=\"Median of a triangle and centroid example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-and-centroid-example.png 360w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-and-centroid-example-300x220.png 300w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><strong><br><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Medians of triangle ABC are AD, BE, and CF. They bisect the opposite sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The points of intersection of medians AD, BE, and CF is known as centroid and it is usually represented by G.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>For the given triangle PQR, G is the centroid and QR <\/strong>$= 12$<strong> inches. Find the length of TR.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"328\" height=\"202\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-and-centroid-example-.png\" alt=\"Median of a triangle and centroid example\" class=\"wp-image-36902\" title=\"Median of a triangle and centroid example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-and-centroid-example-.png 328w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-and-centroid-example--300x185.png 300w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><strong><br><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For the given triangle PQR, PT is the median of the triangle which divides the side QR into two equal parts.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since QR $= 12$ inches (given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, TR $= \\frac{12}{2} = 6$ inches.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>In the given figure, AD is a median, if the area of the triangle ADC is 20 square units, then find the area of the triangle ABD.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"365\" height=\"238\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-.png\" alt=\"Median of a triangle\" class=\"wp-image-36903\" title=\"Median of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-.png 365w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle--300x196.png 300w\" sizes=\"auto, (max-width: 365px) 100vw, 365px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><strong><br><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given: the area of the triangle ADC is 20 square units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the median of a triangle divides the triangle into two triangles having equal area.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the area of the triangle ABD is also 20 square units.<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Determine the length of the median AM of the triangle ABC, whose sides are AB <\/strong>$= 4$<strong> units, BC <\/strong>$= 5$<strong> units, and AC <\/strong>$= 3$<strong> units.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"381\" height=\"226\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-1.png\" alt=\"Median of a triangle\" class=\"wp-image-36904\" title=\"Median of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-1.png 381w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/median-of-a-triangle-1-300x178.png 300w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/figure>\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\"><br>Given: AB $= 4$ units $= c$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">BC $= 5$ units $= a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">AC $= 3$ units $= b$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we have to find the median AM of a triangle $(\\text{i.e}.,\\; m_{a})$. It can be calculated using the formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m_{a} = \\sqrt{\\frac{2b^2 +2c^2\\;-\\;a^2}{4}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow m_{a} = \\sqrt{\\frac{2(3)^{2} + 2(4)^{2}\\;-\\;(5)^{2}}{4}}\\; = \\sqrt{\\frac{18 + 32\\;-\\;25}{4}}\\; = \\sqrt{\\frac{25}{4}}\\;= \\frac{5}{2}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the length of the median AM $= \\frac{5}{2}$ units.<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the length of the median from the vertex A of a triangle ABC, whose vertices are A <\/strong>$(\\;\u2212\\;1,\\; 3)$<strong>, B <\/strong>$(1, \\;\u2212\\;1)$<strong>, and C <\/strong>$(5,\\; 1)$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><strong><br><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given: vertices of triangle ABC are A $(\\;\u22121,\\; 3)$, B $(1, \\;\u22121)$, and C $(5,\\; 1)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 1: Using the midpoint formula, find the midpoint of BC.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For any two points $(x_{1},\\; y_{1})$ and $(x_{2},\\; y_{2})$, midpoint is given by&nbsp; $\\bigg(\\frac{x_{1} + x_{2}}{2},\\; \\frac{y_{1} + y_{2}}{2}\\bigg)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The midpoint of BC $= \\bigg(\\frac{x_{1}+x_{2}}{2},\\; \\frac{y_1+y_2}{2}\\bigg)\\;=\\; \\bigg(\\frac{1+5}{2},\\; \\frac{-1 + 1}{2}\\bigg) = (3, 0)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s say midpoint as point D$(3,\\; 0)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 2: Find the length of median AD using the distance formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For any two points $(x_{1},\\; y_{1})$ and $(x_{2},\\; y_{2})$, distance formula is given by $\\sqrt{(x_{2}\\;-\\;x_{1})^{2} + (y_{2}\\;-\\;y_{1})^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the length of median AD $= \\sqrt{(3\\;-\\;(\\;-1))^{2} + (0\\;-\\; 3)^{2}}\\;=\\;\\sqrt{16 + 9}\\; =\\; \\sqrt{25}\\; = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the length of median AD of triangle ABC $= 5$ units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems-on-median-of-a-triangle\">Practice Problems On Median of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Median of Triangle: Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">In which of the following triangles do the medians have different lengths?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Isosceles<\/div><div class=\"spq_answer_block\" data-value=\"1\">Scalene<\/div><div class=\"spq_answer_block\" data-value=\"2\">Equilateral<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: Scalene<br\/>In a scalene triangle, the medians have different lengths.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The centroid of a triangle is the meeting point of the _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">angle bisectors<\/div><div class=\"spq_answer_block\" data-value=\"1\">altitude<\/div><div class=\"spq_answer_block\" data-value=\"2\">medians<\/div><div class=\"spq_answer_block\" data-value=\"3\">none of these<\/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: medians<br\/>The points where the medians of a triangle meet is known as the centroid.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which line segment represents the altitude of $\\Delta\\text{ABC}?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-3-2.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">AB<\/div><div class=\"spq_answer_block\" data-value=\"1\">AD<\/div><div class=\"spq_answer_block\" data-value=\"2\">DM<\/div><div class=\"spq_answer_block\" data-value=\"3\">AM<\/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: AM<br\/>An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles. In the given figure, AM is the altitude.<\/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\">The three medians of a triangle divide the triangle into how many smaller triangles of equal area?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">4<\/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: 6<br\/>The three medians of a triangle divide the triangle into six smaller triangles of equal area.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">For which of the following triangles are the medians and altitudes the same?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Isosceles<\/div><div class=\"spq_answer_block\" data-value=\"1\">Scalene<\/div><div class=\"spq_answer_block\" data-value=\"2\">Equilateral<\/div><div class=\"spq_answer_block\" data-value=\"3\">All of the above<\/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: Equilateral<br\/>For an equilateral triangle, medians and altitudes are common.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": 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\"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In a scalene triangle, the medians have different lengths.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Isosceles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In a scalene triangle, the medians have different lengths.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Equilateral\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In a scalene triangle, the medians have different lengths.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In a scalene triangle, the medians have different lengths.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Scalene\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In a scalene triangle, the medians have different lengths.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In a scalene triangle, the medians have different lengths.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The centroid of a triangle is the meeting point of the _________.\",\n                    \"text\": \"The centroid of a triangle is the meeting point of the _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The points where the medians of a triangle meet is known as the centroid.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"angle bisectors\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The points where the medians of a triangle meet is known as the centroid.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"altitude\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The points where the medians of a triangle meet is known as the centroid.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"none of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The points where the medians of a triangle meet is known as the centroid.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"medians\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The points where the medians of a triangle meet is known as the centroid.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The points where the medians of a triangle meet is known as the centroid.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which line segment represents the altitude of $$\\\\Delta\\\\text{ABC}?\",\n                    \"text\": \"Which line segment represents the altitude of $$\\\\Delta\\\\text{ABC}? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-3-2.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles. In the given figure, AM is the altitude.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"AB\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles. In the given figure, AM is the altitude.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"AD\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles. In the given figure, AM is the altitude.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"DM\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles. In the given figure, AM is the altitude.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"AM\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles. In the given figure, AM is the altitude.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles. In the given figure, AM is the altitude.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The three medians of a triangle divide the triangle into how many smaller triangles of equal area?\",\n                    \"text\": \"The three medians of a triangle divide the triangle into how many smaller triangles of equal area?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The three medians of a triangle divide the triangle into six smaller triangles of equal area.\"\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\": \"The three medians of a triangle divide the triangle into six smaller triangles of equal area.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The three medians of a triangle divide the triangle into six smaller triangles of equal area.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The three medians of a triangle divide the triangle into six smaller triangles of equal area.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"6\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The three medians of a triangle divide the triangle into six smaller triangles of equal area.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The three medians of a triangle divide the triangle into six smaller triangles of equal area.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"For which of the following triangles are the medians and altitudes the same?\",\n                    \"text\": \"For which of the following triangles are the medians and altitudes the same?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"For an equilateral triangle, medians and altitudes are common.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Isosceles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For an equilateral triangle, medians and altitudes are common.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Scalene\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For an equilateral triangle, medians and altitudes are common.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For an equilateral triangle, medians and altitudes are common.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Equilateral\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"For an equilateral triangle, medians and altitudes are common.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"For an equilateral triangle, medians and altitudes are common.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions-on-median-of-a-triangle\">Frequently Asked Questions On Median of a Triangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\" 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-0-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\"><strong>What is the difference between the median and perpendicular bisector 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-0-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In geometry, a line segment that joins vertices of triangles to the midpoints of opposite sides is called the median of a triangle. A line segment that intersects another line segment at a right angle and divides that other line into two equal parts at its midpoint is known as a perpendicular bisector.<\/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-1-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\"><strong>What is the median of a right 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-1-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In a right triangle, the median drawn from the vertex of the right angle is half the length of the hypotenuse.<\/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-2-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\"><strong>What is the point of intersection of altitudes of a triangle called?<\/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-2-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The points of intersection of altitudes of a triangle are called the orthocenter of the 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-3-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\"><strong>What is incenter in 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-3-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The intersection point of all three interior angle bisectors of a triangle is the incenter. To put it another way, it can be described as the intersection of the triangle\u2019s internal angle bisectors.<\/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-4-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\"><strong>Are the medians of congruent triangles equal?<\/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-4-805e6cac-4a6c-4dcc-a3f8-7dec4d53b835\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, the medians of congruent triangles are equal because the corresponding parts of congruent triangles are congruent.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Median of a Triangle? Triangle is a closed figure with three sides, three interior angles, and three vertices. A median of a triangle is a line segment that joins a vertex to the midpoint of the side that is opposite to that vertex. In the above figure, A, B, and C are &#8230; <a title=\"Median of Triangle: Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/median-of-a-triangle\" aria-label=\"More on Median of Triangle: Definition with 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-25576","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\/25576","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=25576"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25576\/revisions"}],"predecessor-version":[{"id":39915,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25576\/revisions\/39915"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=25576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=25576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=25576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}