{"id":25474,"date":"2023-02-24T07:07:43","date_gmt":"2023-02-24T07:07:43","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=25474"},"modified":"2024-03-14T08:10:53","modified_gmt":"2024-03-14T08:10:53","slug":"diagonals-of-parallelogram-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-parallelogram-formula","title":{"rendered":"Diagonals of Parallelogram: Formula, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-2d0bf483-a005-472c-a125-051421de1d12\" 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\/diagonal-of-parallelogram-formula#0-what-are-diagonals-of-a-parallelogram>What Are Diagonals of a Parallelogram?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-parallelogram-formula#1-properties-of-diagonals-of-a-parallelogram>Properties of Diagonals of a Parallelogram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-parallelogram-formula#2-diagonals-of-parallelogram-formula->Diagonals of Parallelogram Formula&nbsp;&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-parallelogram-formula#7-solved-examples-on-diagonals-of-parallelogram>Solved Examples on Diagonals of Parallelogram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-parallelogram-formula#8-practice-problems-on-diagonals-of-parallelogram>Practice Problems on Diagonals of Parallelogram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-parallelogram-formula#9-frequently-asked-questions-on-diagonals-of-parallelogram>Frequently Asked Questions on Diagonals of Parallelogram<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-diagonals-of-a-parallelogram\">What Are Diagonals of a Parallelogram?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Line segments connecting two non-adjacent vertices of a parallelogram are called \u201cdiagonals of a parallelogram.\u201d&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">A quadrilateral with opposite sides that are parallel and equal is known as a parallelogram. Its opposite angles are also equal.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A parallelogram has two diagonals. The diagonals of a parallelogram connect the opposite vertices.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"366\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/a-parallelogram-and-its-two-diagonals.png\" alt=\"A parallelogram and its two diagonals\" class=\"wp-image-40936\" title=\"A parallelogram and its two diagonals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/a-parallelogram-and-its-two-diagonals.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/a-parallelogram-and-its-two-diagonals-300x177.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Square, rectangle, rhombus are examples of a parallelogram.<\/strong><\/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\/find-volume-using-the-formula\" 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\/geo_meas_vol_formula_pt.png\" alt=\"Find Volume using the Formula 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 Volume using the Formula 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-kite-rhombuses-and-parallelograms\" 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_rhombus_parallelogram_pt.png\" alt=\"Identify Kite, Rhombuses and Parallelograms 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 Kite, Rhombuses and Parallelograms 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-properties-of-diagonals-of-a-parallelogram\">Properties of Diagonals of a Parallelogram<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Diagonals of a parallelogram bisect each other.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The diagonals of a square bisect each other at right angles.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The diagonals of a rectangle bisect each other, but not at right angles.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The diagonals of a rhombus are perpendicular to each other.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Each diagonal divides the parallelogram in two congruent triangles.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-diagonals-of-parallelogram-formula-\">Diagonals of Parallelogram Formula&nbsp;&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s discuss two important formulas.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-finding-lengths-of-diagonals-of-a-parallelogram\">Finding Lengths of Diagonals of a Parallelogram<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"518\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/diagonals-of-a-parallelogram-formulas.png\" alt=\"Diagonals of a parallelogram formulas\" class=\"wp-image-40937\" title=\"Diagonals of a parallelogram formulas\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/diagonals-of-a-parallelogram-formulas.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/diagonals-of-a-parallelogram-formulas-300x251.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The above figure shows a parallelogram and its two diagonals.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">p &amp; q are diagonals.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">x &amp; y are two adjacent sides of a parallelogram.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\angle \\text{A}$ &amp; $\\angle\\text{B}$ are the interior angles of a given parallelogram.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">How can we calculate the length of diagonals of a parallelogram?<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The length of the diagonal of the parallelogram can be calculated by using the following formulas:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>$p = \\sqrt{x^{2} + y^{2}\\;-\\;2xy\\; cos\\;(A)} = \\sqrt{x^{2} + y^{2} + 2xy\\; cos\\;(B)}$<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>$q = \\sqrt{x^{2} + y^{2} + 2xy\\; cos\\;(A)} = \\sqrt{x^{2} + y^{2} \\;-\\; 2xy\\; cos\\;(B)}$<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the measurement of two sides and one interior angle is given the above formula can be used for finding the length of diagonal of the parallelogram.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-relationship-between-sides-and-diagonals-of-a-parallelogram\">Relationship Between Sides and Diagonals of a Parallelogram<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">$p^{2} + q^{2} = 2 (x^{2} + y^{2})$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, Here, p &amp; q are the diagonals of parallelogram<\/p>\n\n\n\n<p class=\"eplus-wrapper\">x &amp; y are the adjacent sides of a parallelogram<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the measurement of two adjacent sides &amp; one diagonal is given then the above formula can be used for finding the length of another diagonal of the parallelogram.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The diagonals of a parallelogram bisect each other at the point of intersection.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The length of the diagonals of a parallelogram is not equal.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">This article gives a brief description of the diagonals of parallelograms, and how to calculate the length of diagonals of parallelograms. Let\u2019s solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-diagonals-of-parallelogram\">Solved Examples on Diagonals of Parallelogram<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Determine the length of diagonals of a parallelogram with side lengths 4 ft, 8 ft,&nbsp; and angle <\/strong>$60^{\\circ}$<strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"293\" height=\"152\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/finding-the-length-of-diagonals-of-a-parallelogram.png\" alt=\"Finding the length of diagonals of a parallelogram\" class=\"wp-image-40938\" title=\"Finding the length of diagonals of a parallelogram\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here x $= 4$&nbsp; ft &amp; y $= 8$&nbsp; ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\text{m} \\angle \\text{A} = 60^{\\circ}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Formula for calculating the length of diagonals is given as,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$p = \\sqrt{x^{2} + y^{2}\\;-\\;2xy\\; cosA}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\sqrt{4^{2} + 8^{2} \\;-\\; 2(4)(8)\\; cos(60^{\\circ})}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 6.92$ ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$q = \\sqrt{x^{2} + y^{2} + 2xy\\; cosA}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$ = \\sqrt{4^{2} + 8^{2} + 2(4)(8)\\; cos(60^{\\circ})}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 10.58$ ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Determine the length of diagonals of a parallelogram with sides 3 inches and 6 inches, and the interior angle is <\/strong><strong>30<\/strong><strong>0<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here,&nbsp; x $= 3$ inches &amp; y $= 6$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Also, &nbsp; $\\text{m}\\;\\angle\\text{A} =30^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Formula for calculating the length of diagonals of the parallelogram is given as,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$p = \\sqrt{x^{2} + y^{2}\\;-\\;2xy\\; cosA}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\sqrt{3^{2} + 6^{2}\\;-\\;2(3)(6)\\; cos\\;30^{\\circ}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 3.71$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$q = \\sqrt{x^{2} + y^{2} + 2xy\\; cosA}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\sqrt{3^{2} + 6^{2} + 2(3)(6)\\; cos\\;(30^{\\circ})}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 8.72$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Determine the length of any one diagonal of a parallelogram if the length of the sides of a parallelogram and interior angle are 4 ft, 7 ft and <\/strong><strong>50<\/strong><strong>o<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given: Here,&nbsp; x $= 4$ ft and y $= 7$&nbsp; ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Also,&nbsp; &nbsp; $\\angle\\text{A} = 50^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Formula for calculating the length of diagonals of the parallelogram is given as,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$p = \\sqrt{x^{2} + y^{2}\\;-\\;2xy\\; cosA}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\sqrt{4^{2} + 7^{2}\\;-\\;2(4)(7)\\; cos(50^{\\circ})}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$=&nbsp; 5.38$ ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Determine the length of any one of the diagonals of a parallelogram having a length of sides 5ft, 7 ft, and one of the interior angles <\/strong><strong>45<\/strong><strong>0<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here,&nbsp; x $= 5$ ft &amp; y $= 7$&nbsp; ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Also,&nbsp; $\\angle\\text{A} = 45^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Formula for calculating the length of diagonals of the parallelogram is given as,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$p = \\sqrt{x^{2} + y^{2}\\;-\\;2xy\\; cos(A)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\sqrt{5^{2} + 7^{2}\\;-\\;2(5)(7)\\; cos(45^{\\circ})}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$=&nbsp; 4.95$ ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Determine the length of a diagonal of&nbsp; a parallelogram with a side length of 5 ft and 8 ft if the length of another diagonal is 10 ft.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given: x $= 5$&nbsp; ft,&nbsp; y $= 8$&nbsp; ft &amp; p $= 10$&nbsp; ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As we know, the length of two sides and one diagonal is given for finding the length of another diagonal. We will use the formula of the relationship between the sides and diagonals of a parallelogram.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">By using the formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$p^{2} + q^{2} = 2(x^{2} + y^{2})$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 10^{2} + q^{2} = 2(5^{2} + 8^{2})$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 100 + q^{2} = 2(25 + 64)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 100 + q^{2} = 178$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow q^{2} = 178\\;-\\;100$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow q^{2} = 78$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">By taking a square root,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow q = 8.83$ ft<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-diagonals-of-parallelogram\">Practice Problems on Diagonals of Parallelogram<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Diagonals of Parallelogram: Formula, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">A parallelogram has _________ diagonals.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">2<\/div><div class=\"spq_answer_block\" data-value=\"3\">1<\/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: 2<br\/>From the 4 vertices of a parallelogram, two diagonals can be drawn connecting two opposite corners.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following statements is not true for parallelogram?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Opposite sides are parallel.<\/div><div class=\"spq_answer_block\" data-value=\"1\">Opposite angles are equal.<\/div><div class=\"spq_answer_block\" data-value=\"2\">It has four vertices.<\/div><div class=\"spq_answer_block\" data-value=\"3\">The length of the diagonal is equal.<\/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: The length of the diagonal is equal.<br\/>The diagonals of the parallelogram are not equal. In the case of a rhombus, square, and rectangle, diagonals are equal.<\/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\">Which of the following is not an example of a parallelogram?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Square<\/div><div class=\"spq_answer_block\" data-value=\"1\">Rectangle<\/div><div class=\"spq_answer_block\" data-value=\"2\">Kite<\/div><div class=\"spq_answer_block\" data-value=\"3\">Rhombus<\/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: Kite<br\/>Kite is not a parallelogram because opposite sides are not parallel and equal.<\/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\">What is the length of the diagonal of a parallelogram with sides 3.5 inches, 6 inches, and interior angle $40^{\\circ}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8.96 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">7.5 inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">5.32 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">4 inches<\/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: 8.96 inches<br\/>Here, x $= 3.5$ in , y $= 6$ in & $\\angle\\text{A} = 40^{\\circ}$<br>\r\n$p = \\sqrt{x^{2} + y^{2}\\;-\\;2xy\\; cosA}$<br>\r\n$= \\sqrt{3.5^{2} + 6^{2}\\;-\\;2(3.5)(6)\\; cos40^{\\circ}}$<br>\r\n$=  8.96$ inches<\/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\">What is the length of one of the diagonals if the length of the sides and one diagonal are 4.5 ft, 7 ft, 9 ft in respectively?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">9.96 ft<\/div><div class=\"spq_answer_block\" data-value=\"1\">10.5 ft<\/div><div class=\"spq_answer_block\" data-value=\"2\">11.02 ft<\/div><div class=\"spq_answer_block\" data-value=\"3\">12.5 ft<\/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: 11.02 ft<br\/>As we know,<br>\r\n$p^{2} + q^{2} = 2(x^{2} + y^{2})$<br>\r\n$9^{2} + q^{2} = 2 (4.5^{2} + 9^{2})$<br>\r\n$81 + q^{2} = 202.5$<br>\r\n$q^{2} = 121.5$<br>\r\n$q=11.02$ ftin<\/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\": \"Diagonals of Parallelogram: Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Diagonals of Parallelogram\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A parallelogram has _________ diagonals.\",\n                    \"text\": \"A parallelogram has _________ diagonals.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"From the 4 vertices of a parallelogram, two diagonals can be drawn connecting two opposite corners.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"From the 4 vertices of a parallelogram, two diagonals can be drawn connecting two opposite corners.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"From the 4 vertices of a parallelogram, two diagonals can be drawn connecting two opposite corners.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"From the 4 vertices of a parallelogram, two diagonals can be drawn connecting two opposite corners.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"From the 4 vertices of a parallelogram, two diagonals can be drawn connecting two opposite corners.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"From the 4 vertices of a parallelogram, two diagonals can be drawn connecting two opposite corners.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following statements is not true for parallelogram?\",\n                    \"text\": \"Which of the following statements is not true for parallelogram?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The diagonals of the parallelogram are not equal. In the case of a rhombus, square, and rectangle, diagonals are equal.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Opposite sides are parallel.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of the parallelogram are not equal. In the case of a rhombus, square, and rectangle, diagonals are equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Opposite angles are equal.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of the parallelogram are not equal. In the case of a rhombus, square, and rectangle, diagonals are equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"It has four vertices.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of the parallelogram are not equal. In the case of a rhombus, square, and rectangle, diagonals are equal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"The length of the diagonal is equal.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The diagonals of the parallelogram are not equal. In the case of a rhombus, square, and rectangle, diagonals are equal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The diagonals of the parallelogram are not equal. In the case of a rhombus, square, and rectangle, diagonals are equal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is not an example of a parallelogram?\",\n                    \"text\": \"Which of the following is not an example of a parallelogram?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Kite is not a parallelogram because opposite sides are not parallel and equal.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Square\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Kite is not a parallelogram because opposite sides are not parallel and equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Rectangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Kite is not a parallelogram because opposite sides are not parallel and equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Rhombus\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Kite is not a parallelogram because opposite sides are not parallel and equal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Kite\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Kite is not a parallelogram because opposite sides are not parallel and equal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Kite is not a parallelogram because opposite sides are not parallel and equal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the length of the diagonal of a parallelogram with sides 3.5 inches, 6 inches, and interior angle $$40^{\\\\circ}$$?\",\n                    \"text\": \"What is the length of the diagonal of a parallelogram with sides 3.5 inches, 6 inches, and interior angle $$40^{\\\\circ}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Here, x $$= 3.5$$ in , y $$= 6$$ in & $$\\\\angle\\\\text{A} = 40^{\\\\circ}$$<br>\r\n$$p = \\\\sqrt{x^{2} + y^{2}\\\\;-\\\\;2xy\\\\; cosA}$$<br>\r\n$$= \\\\sqrt{3.5^{2} + 6^{2}\\\\;-\\\\;2(3.5)(6)\\\\; cos40^{\\\\circ}}$$<br>\r\n$$=  8.96$$ inches\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"7.5 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, x $$= 3.5$$ in , y $$= 6$$ in & $$\\\\angle\\\\text{A} = 40^{\\\\circ}$$<br>\r\n$$p = \\\\sqrt{x^{2} + y^{2}\\\\;-\\\\;2xy\\\\; cosA}$$<br>\r\n$$= \\\\sqrt{3.5^{2} + 6^{2}\\\\;-\\\\;2(3.5)(6)\\\\; cos40^{\\\\circ}}$$<br>\r\n$$=  8.96$$ inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5.32 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, x $$= 3.5$$ in , y $$= 6$$ in & $$\\\\angle\\\\text{A} = 40^{\\\\circ}$$<br>\r\n$$p = \\\\sqrt{x^{2} + y^{2}\\\\;-\\\\;2xy\\\\; cosA}$$<br>\r\n$$= \\\\sqrt{3.5^{2} + 6^{2}\\\\;-\\\\;2(3.5)(6)\\\\; cos40^{\\\\circ}}$$<br>\r\n$$=  8.96$$ inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, x $$= 3.5$$ in , y $$= 6$$ in & $$\\\\angle\\\\text{A} = 40^{\\\\circ}$$<br>\r\n$$p = \\\\sqrt{x^{2} + y^{2}\\\\;-\\\\;2xy\\\\; cosA}$$<br>\r\n$$= \\\\sqrt{3.5^{2} + 6^{2}\\\\;-\\\\;2(3.5)(6)\\\\; cos40^{\\\\circ}}$$<br>\r\n$$=  8.96$$ inches\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8.96 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Here, x $$= 3.5$$ in , y $$= 6$$ in & $$\\\\angle\\\\text{A} = 40^{\\\\circ}$$<br>\r\n$$p = \\\\sqrt{x^{2} + y^{2}\\\\;-\\\\;2xy\\\\; cosA}$$<br>\r\n$$= \\\\sqrt{3.5^{2} + 6^{2}\\\\;-\\\\;2(3.5)(6)\\\\; cos40^{\\\\circ}}$$<br>\r\n$$=  8.96$$ inches\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Here, x $$= 3.5$$ in , y $$= 6$$ in & $$\\\\angle\\\\text{A} = 40^{\\\\circ}$$<br>\r\n$$p = \\\\sqrt{x^{2} + y^{2}\\\\;-\\\\;2xy\\\\; cosA}$$<br>\r\n$$= \\\\sqrt{3.5^{2} + 6^{2}\\\\;-\\\\;2(3.5)(6)\\\\; cos40^{\\\\circ}}$$<br>\r\n$$=  8.96$$ inches\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the length of one of the diagonals if the length of the sides and one diagonal are 4.5 ft, 7 ft, 9 ft in respectively?\",\n                    \"text\": \"What is the length of one of the diagonals if the length of the sides and one diagonal are 4.5 ft, 7 ft, 9 ft in respectively?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"As we know,<br>\r\n$$p^{2} + q^{2} = 2(x^{2} + y^{2})$$<br>\r\n$$9^{2} + q^{2} = 2 (4.5^{2} + 9^{2})$$<br>\r\n$$81 + q^{2} = 202.5$$<br>\r\n$$q^{2} = 121.5$$<br>\r\n$$q=11.02$$ ftin\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9.96 ft\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As we know,<br>\r\n$$p^{2} + q^{2} = 2(x^{2} + y^{2})$$<br>\r\n$$9^{2} + q^{2} = 2 (4.5^{2} + 9^{2})$$<br>\r\n$$81 + q^{2} = 202.5$$<br>\r\n$$q^{2} = 121.5$$<br>\r\n$$q=11.02$$ ftin\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10.5 ft\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As we know,<br>\r\n$$p^{2} + q^{2} = 2(x^{2} + y^{2})$$<br>\r\n$$9^{2} + q^{2} = 2 (4.5^{2} + 9^{2})$$<br>\r\n$$81 + q^{2} = 202.5$$<br>\r\n$$q^{2} = 121.5$$<br>\r\n$$q=11.02$$ ftin\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12.5 ft\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As we know,<br>\r\n$$p^{2} + q^{2} = 2(x^{2} + y^{2})$$<br>\r\n$$9^{2} + q^{2} = 2 (4.5^{2} + 9^{2})$$<br>\r\n$$81 + q^{2} = 202.5$$<br>\r\n$$q^{2} = 121.5$$<br>\r\n$$q=11.02$$ ftin\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"11.02 ft\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"As we know,<br>\r\n$$p^{2} + q^{2} = 2(x^{2} + y^{2})$$<br>\r\n$$9^{2} + q^{2} = 2 (4.5^{2} + 9^{2})$$<br>\r\n$$81 + q^{2} = 202.5$$<br>\r\n$$q^{2} = 121.5$$<br>\r\n$$q=11.02$$ ftin\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"As we know,<br>\r\n$$p^{2} + q^{2} = 2(x^{2} + y^{2})$$<br>\r\n$$9^{2} + q^{2} = 2 (4.5^{2} + 9^{2})$$<br>\r\n$$81 + q^{2} = 202.5$$<br>\r\n$$q^{2} = 121.5$$<br>\r\n$$q=11.02$$ ftin\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-diagonals-of-parallelogram\">Frequently Asked Questions on Diagonals of Parallelogram<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b2743529-7648-473e-b7ce-313e1cf51d94\" 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-b2743529-7648-473e-b7ce-313e1cf51d94\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2743529-7648-473e-b7ce-313e1cf51d94\"><strong>Are diagonals of a parallelogram 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-0-b2743529-7648-473e-b7ce-313e1cf51d94\">\n\n<p class=\"eplus-wrapper\">Diagonals of a parallelogram bisect each other, but they are not 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-b2743529-7648-473e-b7ce-313e1cf51d94\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2743529-7648-473e-b7ce-313e1cf51d94\"><strong>Which parallelogram has equal diagonals?<\/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-b2743529-7648-473e-b7ce-313e1cf51d94\">\n\n<p class=\"eplus-wrapper\">A rectangle has equal diagonals which bisect each other and are perpendicular.<\/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-b2743529-7648-473e-b7ce-313e1cf51d94\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2743529-7648-473e-b7ce-313e1cf51d94\"><strong>Are diagonals of parallelograms perpendicular?<\/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-b2743529-7648-473e-b7ce-313e1cf51d94\">\n\n<p class=\"eplus-wrapper\">No, diagonals of a parallelogram bisect each other but not necessarily at $90^{\\circ}$.<\/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-b2743529-7648-473e-b7ce-313e1cf51d94\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2743529-7648-473e-b7ce-313e1cf51d94\"><strong>What is parallelogram law?<\/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-b2743529-7648-473e-b7ce-313e1cf51d94\">\n\n<p class=\"eplus-wrapper\">The parallelogram law states that the sum of the squares of the length of the four sides of a parallelogram is equal to the sum of the squares of the length of the two diagonals.<\/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-b2743529-7648-473e-b7ce-313e1cf51d94\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2743529-7648-473e-b7ce-313e1cf51d94\"><strong>What is the formula for calculating the number of diagonals of a quadrilateral?<\/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-b2743529-7648-473e-b7ce-313e1cf51d94\">\n\n<p class=\"eplus-wrapper\">The number of diagonals of any quadrilateral can be calculated using the formula $\\frac{n(n-3)}{2}$, where n is the number of sides of a given polygon.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Diagonals of a Parallelogram? Line segments connecting two non-adjacent vertices of a parallelogram are called \u201cdiagonals of a parallelogram.\u201d&nbsp; A quadrilateral with opposite sides that are parallel and equal is known as a parallelogram. Its opposite angles are also equal.&nbsp; A parallelogram has two diagonals. The diagonals of a parallelogram connect the opposite &#8230; <a title=\"Diagonals of Parallelogram: Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-parallelogram-formula\" aria-label=\"More on Diagonals of Parallelogram: Formula, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-25474","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\/25474","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=25474"}],"version-history":[{"count":17,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25474\/revisions"}],"predecessor-version":[{"id":40939,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25474\/revisions\/40939"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=25474"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=25474"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=25474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}