{"id":25784,"date":"2023-03-03T05:17:50","date_gmt":"2023-03-03T05:17:50","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=25784"},"modified":"2023-09-12T06:16:04","modified_gmt":"2023-09-12T06:16:04","slug":"isosceles-right-triangle-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-right-triangle","title":{"rendered":"Isosceles Right 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-3f5275c4-e4ea-447c-91c3-2778463dc462\" 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\/isosceles-right-triangle#0-what-is-an-isosceles-right-triangle>What Is an Isosceles Right Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-right-triangle#3-how-to-find-the-hypotenuse-of-an-isosceles-triangle>How to Find the Hypotenuse of an Isosceles Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-right-triangle#4-isosceles-right-triangle-formulas>Isosceles Right Triangle Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-right-triangle#10-solved-examples-on-isosceles-right>Solved Examples on Isosceles Right<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-right-triangle#11-practice-problems-on-isosceles-right-triangle>Practice Problems on Isosceles Right Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-right-triangle#12-frequently-asked-questions-on-isosceles-right-triangle>Frequently Asked Questions on Isosceles Right Triangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-an-isosceles-right-triangle\">What Is an Isosceles Right Triangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>An isosceles right triangle is a right-angled triangle whose base and height (legs) are equal in length<\/strong>. It is a type of special isosceles triangle where one interior angle is a right angle and the remaining two angles are thus congruent since the angles opposite to the equal sides are equal.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is also known by the name of <strong>right-angled isosceles triangle<\/strong> or a right isosceles triangle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"431\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-1.png\" alt=\"Right triangle and isosceles triangle\" class=\"wp-image-25807\" title=\"Right triangle and isosceles triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-1-300x209.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When you combine these two properties together, you get an isosceles right triangle.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-isosceles-right-triangle-definition\">Isosceles Right Triangle: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An isosceles right triangle is a type of right triangle whose legs (base and height) are equal in length.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the two sides of the right triangle are equal in measure, the corresponding angles are also equal. Therefore, in an isosceles right triangle, two sides and the two acute angles are equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the interior angles of an isosceles right triangle are $90^{\\circ},\\; 45^{\\circ},\\;45^{\\circ}$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"521\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-2.png\" alt=\"Isosceles right triangle\" class=\"wp-image-25808\" title=\"Isosceles right triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-2-300x252.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\/find-right-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_identify_right_angle_1_pt.png\" alt=\"Find Right 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\">Find Right 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-if-the-given-angle-is-right-acute-or-obtuse\" 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_identify_type_of_angle_pt.png\" alt=\"Identify if the Given Angle is Right, Acute or Obtuse 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 if the Given Angle is Right, Acute or Obtuse 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-right-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_identify_right_angle_2_pt.png\" alt=\"Identify Right 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 Right 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-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><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=\"2-isosceles-right-triangle-hypotenuse\">Isosceles Right Triangle Hypotenuse<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The hypotenuse of a right angled triangle is the longest side of the triangle, which is opposite to the right angle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is equal to exactly $\u221a2$ times the length of the congruent sides of the triangle. If the length of each of the equal sides is x units, then the length of the hypotenuse of the isosceles right triangle will be equal to $\\sqrt{2x}$ units.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This property is derived using the Pythagoras\u2019 theorem. Here\u2019s a right triangle, $\\Delta PQR$:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"660\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-4.png\" alt=\"Isosceles right triangle hypotenuse formula\" class=\"wp-image-25809\" title=\"Isosceles right triangle hypotenuse formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-4-282x300.png 282w\" 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 eplus-wrapper\" id=\"3-how-to-find-the-hypotenuse-of-an-isosceles-triangle\">How to Find the Hypotenuse of an Isosceles Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the hypotenuse of an isosceles right triangle, we use the Pythagorean theorem.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"533\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-5.png\" alt=\"Hypotenuse and sides of the isosceles right triangle\" class=\"wp-image-25811\" title=\"Hypotenuse and sides of the isosceles right triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-5-300x258.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that in an isosceles right triangle, two sides are of equal length.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, if we assume both the sides to be equal to x units, the hypotenuse can be calculated as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Hypotenuse^{2} = x^{2} + x^{2}$ _______________(By Pythagoras\u2019 theorem)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Hypotenuse^{2} = 2x^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Hypotenuse= \\sqrt{2x^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Hypotenuse= \\sqrt{2}x$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can use the above derived result as it is without applying the Pythagoras\u2019 theorem every time. The length of the hypotenuse of an isosceles right triangle will always be equal to $\u221a2$ times the length of the equal sides of the triangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-isosceles-right-triangle-formulas\">Isosceles Right Triangle Formulas<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We just discussed the formula to find the hypotenuse of an isosceles right triangle. It is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hypotenuse $= \\sqrt{2} \\times$ Length of congruent sides<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now let\u2019s discuss the formulas to find the perimeter and area of the right angled isosceles triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"524\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-6.png\" alt=\"Isosceles Right Triangle PQR\" class=\"wp-image-25812\" title=\"Isosceles Right Triangle PQR\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Isosceles-Right-Triangle-6-300x254.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-area-of-an-isosceles-right-triangle\">Area of an Isosceles Right Triangle<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of a triangle $= \\frac{1}{2} \\times$ Base $\\times$ Height.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In $\\Delta PQR ,\\; PQ = QR = x$, where PQ is the height and QR is the base.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The area of the isosceles right triangle $= \\frac{1}{2} \\times PQ \\times QR$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$= \\frac{x \\times x}{2}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;$= \\frac{x^{2}}{2}$ sq. units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the area of the isosceles right triangle formula is $\\frac{x^{2}}{2}$, where \u201cx\u201d is equal to the congruent side length.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-perimeter-of-an-isosceles-right-triangle\">Perimeter of an Isosceles Right Triangle<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of a triangle $=$ Sum of lengths of all its sides<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of isosceles right triangle $\\Delta PQR = PQ + QR + PR$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PQ = QR = x$ units&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PR = h$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of the isosceles right triangle formula $= x + x + h = (2x + h)$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the perimeter of the isosceles right triangle formula is $2x + h$, where \u201cx\u201d represents the length of congruent sides and \u201ch\u201d is equal to the length of the hypotenuse.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-isosceles-right-triangle-properties\">Isosceles Right Triangle Properties<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">It has one interior angle, which is equal to $90^{\\circ}$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The sides or legs are perpendicular to each other and are also known as the base and the height. They are congruent.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The other two angles of an isosceles right triangle are acute angles and are congruent to each other. They are equal to $45^{\\circ}$ each.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The sum of all the interior angles measures $180^{\\circ}$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If we draw an altitude from the right angle vertex to the hypotenuse (the opposite side), then it is the perpendicular bisector of the hypotenuse.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The area of an isosceles right triangle is equal to $12 \\times$ Base $\\times$ Height square units.<\/li>\n<\/ol>\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\">Since the two sides of an isosceles right triangle are equal, the angles are also equal. And both the angles measure 45 degrees.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Right angle is always the largest angle in a right triangle.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">There can&#8217;t be any obtuse angles in a right triangle.<\/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 explored the properties of the isosceles right triangle. Let\u2019s solve some practice problems for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples-on-isosceles-right\">Solved Examples on Isosceles Right<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. The equal sides of an isosceles right triangle are 5 units each. Calculate the length of its hypotenuse.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the formula to calculate the hypotenuse of an isosceles right triangle is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hypotenuse $= \\sqrt{2\\; x}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where, \u201cx\u201d is the length of the congruent side.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The equal sides measure 5 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the hypotenuse will be equal to $\\sqrt{2 \\times 5} = 7.071$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. The length of the base of an isosceles right triangle is 10 units. What will be the area of this triangle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the formula to calculate the area of an isosceles right triangle is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{x^{2}}{2}$ square units, where x is the measure of the congruent side of the triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area $= \\frac{10^{2}}{2} = \\frac{100}{2} = 50$ square units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. The area of an isosceles right triangle is 72 square units. What is the measure of its base?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the formula to calculate the area of an isosceles right triangle is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{x^{2}}{2}$ square units, where x is the measure of the congruent side of the triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given that the area of the triangle is 72 square units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Putting this value in the formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{x^{2}}{2} = 72$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x^{2} = 72 \\times 2 = 144$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = \\sqrt{144}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 12$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the measure of the base of an isosceles right triangle with area equal to 72 square units is 12 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. The height of a right isosceles triangle is 8 units. What will be its perimeter?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The perimeter of an isosceles right triangle $= (2x + h)$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">x is equal to the length of the congruent side<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">h is the measure of the hypotenuse.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The height of this isosceles right triangle is 8 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Hypotenuse = \\sqrt{2x}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$h = \\sqrt{2 \\times 8} = 11.3137$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Perimeter = 2x + h = (2 \\times 8) + 11.3137 = 27.3137$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. The perimeter of an isosceles right triangle is equal to <\/strong>$10 + 5\\sqrt{2}$<strong> units. If the non-congruent side is equal to <\/strong>$5\\sqrt{2}$<strong> units then, find the measure of the congruent sides.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the formula to calculate the perimeter of an isosceles right triangle is: $(2x + h)$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Where, x is equal to the length of the congruent side and h is the measure of the hypotenuse.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Perimeter = 10 + 5\\sqrt{2}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hypotenuse $= 5\\sqrt{2}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Putting this in the above formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$10 + 5\\sqrt{2} = 2x + 5\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$10 = 2x$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 5$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the congruent side is equal to 5 units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems-on-isosceles-right-triangle\">Practice Problems on Isosceles Right Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Isosceles Right Triangle: Definition with 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\">The equal sides of an isosceles right triangle are 7 units each. What is the length of its hypotenuse?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">9 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">10 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">14 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: 10 units<br\/>Hypotenuse $= \\sqrt{2x}$<br>\r\nwhere, x is the length of the congruent side.<br>\r\nGiven that, the equal sides measure 7 units.<br>\r\nTherefore, the hypotenuse will be equal to $\\sqrt{2 \\times 7} = 9.8994 \\approx 10$ units.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The length of the base of an isosceles right triangle is 10 units. What will be the area of this triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">50 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"1\">50.5 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"2\">100.5 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"3\">100 sq. 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: 50 sq. units<br\/>Area of an isosceles right triangle $= \\frac{x^{2}}{2}$ square units, where x is the length of the congruent sides of the triangle.<br>\r\nHere, $x = 10$ units.\r\nArea $= \\frac{10^{2}}{2} = \\frac{100}{2} = 50$ square units.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The area of an isosceles right triangle is 32 square units. What is the measure of its base?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"1\">15 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"2\">8 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"3\">50 sq. 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: 8 sq. units<br\/>Area of an isosceles right triangle = x22 square units, where x is the length of the congruent sides of the triangle.<br>\r\n$\\frac{x^{2}}{2} = 32$<br>\r\n$x^{2} = 32 \\times 2 = 64$<br>\r\n$x = \\sqrt{64}$<br>\r\n$x = 8\\;$ units<br>\r\nTherefore, the measure of the base of an isosceles right triangle with area equal to 32 square units is 8 units.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The area of the isosceles right triangle whose base and height equal 1 unit is ____________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{2}$ sq. units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$2$ sq. units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{4}$ sq. units<\/div><div class=\"spq_answer_block\" data-value=\"3\">$4$ sq. 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: $\\frac{1}{2}$ sq. units<br\/>Area of isosceles right triangle $=  \\frac{x^{2}}{2} = \\frac{1}{2}$ sq. units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The hypotenuse of the isosceles right triangle whose equal sides are given by x units is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\sqrt{3x}$ units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\sqrt{2x}$ units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2x$ units<\/div><div class=\"spq_answer_block\" data-value=\"3\">$x$ 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: $\\sqrt{2x}$ units<br\/>The hypotenuse of the isosceles right triangle is given by $\\sqrt{2x}$, where x represents the length of the congruent sides.<\/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\": \"Isosceles Right Triangle: Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Isosceles Right Triangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The equal sides of an isosceles right triangle are 7 units each. 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What is the length of its hypotenuse?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Hypotenuse $$= \\\\sqrt{2x}$$<br>\r\nwhere, x is the length of the congruent side.<br>\r\nGiven that, the equal sides measure 7 units.<br>\r\nTherefore, the hypotenuse will be equal to $$\\\\sqrt{2 \\\\times 7} = 9.8994 \\\\approx 10$$ units.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse $$= \\\\sqrt{2x}$$<br>\r\nwhere, x is the length of the congruent side.<br>\r\nGiven that, the equal sides measure 7 units.<br>\r\nTherefore, the hypotenuse will be equal to $$\\\\sqrt{2 \\\\times 7} = 9.8994 \\\\approx 10$$ units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse $$= \\\\sqrt{2x}$$<br>\r\nwhere, x is the length of the congruent side.<br>\r\nGiven that, the equal sides measure 7 units.<br>\r\nTherefore, the hypotenuse will be equal to $$\\\\sqrt{2 \\\\times 7} = 9.8994 \\\\approx 10$$ units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse $$= \\\\sqrt{2x}$$<br>\r\nwhere, x is the length of the congruent side.<br>\r\nGiven that, the equal sides measure 7 units.<br>\r\nTherefore, the hypotenuse will be equal to $$\\\\sqrt{2 \\\\times 7} = 9.8994 \\\\approx 10$$ units.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"10 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Hypotenuse $$= \\\\sqrt{2x}$$<br>\r\nwhere, x is the length of the congruent side.<br>\r\nGiven that, the equal sides measure 7 units.<br>\r\nTherefore, the hypotenuse will be equal to $$\\\\sqrt{2 \\\\times 7} = 9.8994 \\\\approx 10$$ units.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Hypotenuse $$= \\\\sqrt{2x}$$<br>\r\nwhere, x is the length of the congruent side.<br>\r\nGiven that, the equal sides measure 7 units.<br>\r\nTherefore, the hypotenuse will be equal to $$\\\\sqrt{2 \\\\times 7} = 9.8994 \\\\approx 10$$ units.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The length of the base of an isosceles right triangle is 10 units. What will be the area of this triangle?\",\n                    \"text\": \"The length of the base of an isosceles right triangle is 10 units. What will be the area of this triangle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of an isosceles right triangle $$= \\\\frac{x^{2}}{2}$$ square units, where x is the length of the congruent sides of the triangle.<br>\r\nHere, $$x = 10$$ units.\r\nArea $$= \\\\frac{10^{2}}{2} = \\\\frac{100}{2} = 50$$ square units.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50.5 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of an isosceles right triangle $$= \\\\frac{x^{2}}{2}$$ square units, where x is the length of the congruent sides of the triangle.<br>\r\nHere, $$x = 10$$ units.\r\nArea $$= \\\\frac{10^{2}}{2} = \\\\frac{100}{2} = 50$$ square units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100.5 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of an isosceles right triangle $$= \\\\frac{x^{2}}{2}$$ square units, where x is the length of the congruent sides of the triangle.<br>\r\nHere, $$x = 10$$ units.\r\nArea $$= \\\\frac{10^{2}}{2} = \\\\frac{100}{2} = 50$$ square units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of an isosceles right triangle $$= \\\\frac{x^{2}}{2}$$ square units, where x is the length of the congruent sides of the triangle.<br>\r\nHere, $$x = 10$$ units.\r\nArea $$= \\\\frac{10^{2}}{2} = \\\\frac{100}{2} = 50$$ square units.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"50 sq. units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of an isosceles right triangle $$= \\\\frac{x^{2}}{2}$$ square units, where x is the length of the congruent sides of the triangle.<br>\r\nHere, $$x = 10$$ units.\r\nArea $$= \\\\frac{10^{2}}{2} = \\\\frac{100}{2} = 50$$ square units.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of an isosceles right triangle $$= \\\\frac{x^{2}}{2}$$ square units, where x is the length of the congruent sides of the triangle.<br>\r\nHere, $$x = 10$$ units.\r\nArea $$= \\\\frac{10^{2}}{2} = \\\\frac{100}{2} = 50$$ square units.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The area of an isosceles right triangle is 32 square units. What is the measure of its base?\",\n                    \"text\": \"The area of an isosceles right triangle is 32 square units. What is the measure of its base?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of an isosceles right triangle = x22 square units, where x is the length of the congruent sides of the triangle.<br>\r\n$$\\\\frac{x^{2}}{2} = 32$$<br>\r\n$$x^{2} = 32 \\\\times 2 = 64$$<br>\r\n$$x = \\\\sqrt{64}$$<br>\r\n$$x = 8\\\\;$$ units<br>\r\nTherefore, the measure of the base of an isosceles right triangle with area equal to 32 square units is 8 units.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of an isosceles right triangle = x22 square units, where x is the length of the congruent sides of the triangle.<br>\r\n$$\\\\frac{x^{2}}{2} = 32$$<br>\r\n$$x^{2} = 32 \\\\times 2 = 64$$<br>\r\n$$x = \\\\sqrt{64}$$<br>\r\n$$x = 8\\\\;$$ units<br>\r\nTherefore, the measure of the base of an isosceles right triangle with area equal to 32 square units is 8 units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of an isosceles right triangle = x22 square units, where x is the length of the congruent sides of the triangle.<br>\r\n$$\\\\frac{x^{2}}{2} = 32$$<br>\r\n$$x^{2} = 32 \\\\times 2 = 64$$<br>\r\n$$x = \\\\sqrt{64}$$<br>\r\n$$x = 8\\\\;$$ units<br>\r\nTherefore, the measure of the base of an isosceles right triangle with area equal to 32 square units is 8 units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of an isosceles right triangle = x22 square units, where x is the length of the congruent sides of the triangle.<br>\r\n$$\\\\frac{x^{2}}{2} = 32$$<br>\r\n$$x^{2} = 32 \\\\times 2 = 64$$<br>\r\n$$x = \\\\sqrt{64}$$<br>\r\n$$x = 8\\\\;$$ units<br>\r\nTherefore, the measure of the base of an isosceles right triangle with area equal to 32 square units is 8 units.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8 sq. units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of an isosceles right triangle = x22 square units, where x is the length of the congruent sides of the triangle.<br>\r\n$$\\\\frac{x^{2}}{2} = 32$$<br>\r\n$$x^{2} = 32 \\\\times 2 = 64$$<br>\r\n$$x = \\\\sqrt{64}$$<br>\r\n$$x = 8\\\\;$$ units<br>\r\nTherefore, the measure of the base of an isosceles right triangle with area equal to 32 square units is 8 units.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of an isosceles right triangle = x22 square units, where x is the length of the congruent sides of the triangle.<br>\r\n$$\\\\frac{x^{2}}{2} = 32$$<br>\r\n$$x^{2} = 32 \\\\times 2 = 64$$<br>\r\n$$x = \\\\sqrt{64}$$<br>\r\n$$x = 8\\\\;$$ units<br>\r\nTherefore, the measure of the base of an isosceles right triangle with area equal to 32 square units is 8 units.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The area of the isosceles right triangle whose base and height equal 1 unit is ____________.\",\n                    \"text\": \"The area of the isosceles right triangle whose base and height equal 1 unit is ____________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of isosceles right triangle $$=  \\\\frac{x^{2}}{2} = \\\\frac{1}{2}$$ sq. units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2$$ sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of isosceles right triangle $$=  \\\\frac{x^{2}}{2} = \\\\frac{1}{2}$$ sq. units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{4}$$ sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of isosceles right triangle $$=  \\\\frac{x^{2}}{2} = \\\\frac{1}{2}$$ sq. units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4$$ sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of isosceles right triangle $$=  \\\\frac{x^{2}}{2} = \\\\frac{1}{2}$$ sq. units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{2}$$ sq. units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of isosceles right triangle $$=  \\\\frac{x^{2}}{2} = \\\\frac{1}{2}$$ sq. units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of isosceles right triangle $$=  \\\\frac{x^{2}}{2} = \\\\frac{1}{2}$$ sq. units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The hypotenuse of the isosceles right triangle whose equal sides are given by x units is\",\n                    \"text\": \"The hypotenuse of the isosceles right triangle whose equal sides are given by x units is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The hypotenuse of the isosceles right triangle is given by $$\\\\sqrt{2x}$$, where x represents the length of the congruent sides.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{3x}$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The hypotenuse of the isosceles right triangle is given by $$\\\\sqrt{2x}$$, where x represents the length of the congruent sides.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2x$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The hypotenuse of the isosceles right triangle is given by $$\\\\sqrt{2x}$$, where x represents the length of the congruent sides.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The hypotenuse of the isosceles right triangle is given by $$\\\\sqrt{2x}$$, where x represents the length of the congruent sides.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\sqrt{2x}$$ units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The hypotenuse of the isosceles right triangle is given by $$\\\\sqrt{2x}$$, where x represents the length of the congruent sides.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The hypotenuse of the isosceles right triangle is given by $$\\\\sqrt{2x}$$, where x represents the length of the congruent sides.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions-on-isosceles-right-triangle\">Frequently Asked Questions on Isosceles Right Triangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-8b95696d-28b1-4463-943e-18065666addb\" 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-0-8b95696d-28b1-4463-943e-18065666addb\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b95696d-28b1-4463-943e-18065666addb\"><strong>Are all isosceles right triangles <\/strong>$45^{\\circ}\\;-\\;45^{\\circ}\\;-\\;90^{\\circ}$<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-0-8b95696d-28b1-4463-943e-18065666addb\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, all the isosceles right triangles have interior angles measuring $45^{\\circ},\\; 45^{\\circ},\\;$ and $90^{\\circ}$. This is because one angle has to be a right angle (90 degree), and consequently, the other two angles have to be equal as the opposite sides 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-1-8b95696d-28b1-4463-943e-18065666addb\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b95696d-28b1-4463-943e-18065666addb\"><strong>What are the types of triangles based on length of sides?<\/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-1-8b95696d-28b1-4463-943e-18065666addb\">\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Isosceles triangle: Two sides are congruent.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Equilateral triangle: All sides are congruent.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Scalene triangle: All sides are of different lengths.<\/li>\n<\/ul>\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-2-8b95696d-28b1-4463-943e-18065666addb\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b95696d-28b1-4463-943e-18065666addb\"><strong>What is an acute angled 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-2-8b95696d-28b1-4463-943e-18065666addb\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle that has all angles measuring less than 90 degrees is called an acute-angled 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-3-8b95696d-28b1-4463-943e-18065666addb\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b95696d-28b1-4463-943e-18065666addb\"><strong>What is an obtuse angled 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-3-8b95696d-28b1-4463-943e-18065666addb\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle that has one of its angles going beyond 90 degrees, is called an obtuse-angled 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-4-8b95696d-28b1-4463-943e-18065666addb\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b95696d-28b1-4463-943e-18065666addb\"><strong>What are three types of isosceles triangles?<\/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-4-8b95696d-28b1-4463-943e-18065666addb\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Isosceles triangles can be classified into three types: 1) acute isosceles triangle, 2) obtuse isosceles triangle, and 3) right isosceles triangles.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is an Isosceles Right Triangle? An isosceles right triangle is a right-angled triangle whose base and height (legs) are equal in length. It is a type of special isosceles triangle where one interior angle is a right angle and the remaining two angles are thus congruent since the angles opposite to the equal sides &#8230; <a title=\"Isosceles Right Triangle: Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-right-triangle\" aria-label=\"More on Isosceles Right 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-25784","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\/25784","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=25784"}],"version-history":[{"count":19,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25784\/revisions"}],"predecessor-version":[{"id":34004,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25784\/revisions\/34004"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=25784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=25784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=25784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}