{"id":4531,"date":"2013-06-29T06:39:10","date_gmt":"2013-06-29T06:39:10","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4531"},"modified":"2026-03-26T09:51:51","modified_gmt":"2026-03-26T14:51:51","slug":"pythagorean-theorem","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/pythagorean-theorem\/","title":{"rendered":"Pythagorean Theorem"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_8v6zQKtvLP8\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_8v6zQKtvLP8\" data-source-videoID=\"8v6zQKtvLP8\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Pythagorean Theorem Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Pythagorean Theorem\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_8v6zQKtvLP8:hover {cursor:pointer;} img#videoThumbnailImage_8v6zQKtvLP8 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/702-pythagorean-theorem-1-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_8v6zQKtvLP8\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_8v6zQKtvLP8\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Pythagorean Theorem\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_8v6zQKtvLP8\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_8v6zQKtvLP8\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_8v6zQKtvLP8\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction 9qm_Function() {\n  var x = document.getElementById(\"9qm\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"9qm_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"9qm\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Pythagorean_Theorem_Formula\" class=\"smooth-scroll\">Pythagorean Theorem Formula<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Applying_the_Pythagorean_Theorem_to_a_Triangle\" class=\"smooth-scroll\">Applying the Pythagorean Theorem to a Triangle<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Triangle_Inequality_Theorem\" class=\"smooth-scroll\">Triangle Inequality Theorem<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Pythagorean_Triples\" class=\"smooth-scroll\">Pythagorean Triples<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Final_Example\" class=\"smooth-scroll\">Final Example<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Pythagorean_Theorem_Practice_Problems\" class=\"smooth-scroll\">Pythagorean Theorem Practice Problems<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Pythagorean_Theorem_Worksheets\" class=\"smooth-scroll\">Pythagorean Theorem Worksheets<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label><input id=\"worksheets\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"worksheets\">Worksheets<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this review of the Pythagorean theorem! We\u2019re going to go over how to use it properly and also go over some special <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/introduction-to-types-of-triangles\/\">triangles<\/a> called \u201cPythagorean triples\u201d that could save you some time when taking tests. So, let\u2019s get started! <\/p>\n<h2><span id=\"Pythagorean_Theorem_Formula\" class=\"m-toc-anchor\"><\/span>Pythagorean Theorem Formula<\/h2>\n<p>\nFirst thing\u2019s first: what is the Pythagorean theorem? The Pythagorean theorem is \\(a^2+b^2=c^2\\).<\/p>\n<p>Now, this is used to find the length of a side of a right triangle when we know the length of the other two sides. The triangle has to be a right triangle, which means that it has an angle that measures exactly 90 degrees, like this one:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square.png\" alt=\"A right triangle with a small square indicating the right angle\" width=\"200\" height=\"199.227\" class=\"aligncenter size-full wp-image-93520\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square.png 745w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-300x300.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-150x150.png 150w\" sizes=\"(max-width: 745px) 100vw, 745px\" \/><\/p>\n<p>The theorem is very easy to remember and just as easy to use! In the theorem, \\(a\\), \\(b\\), and \\(c\\) are the lengths of the three sides of the triangle. But which is which? Let\u2019s start by figuring out where to find \\(a\\), \\(b\\), and \\(c\\) in a triangle.<\/p>\n<h2><span id=\"Applying_the_Pythagorean_Theorem_to_a_Triangle\" class=\"m-toc-anchor\"><\/span>Applying the Pythagorean Theorem to a Triangle<\/h2>\n<p>\nTo start, you can tell that you\u2019re dealing with a right triangle because you can see this little square in one of the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/angles\/\">angles<\/a>. That\u2019s the symbol for a right angle (or 90\u02da angle). Any triangle that has a right angle must be a right triangle. <\/p>\n<p>So now we have to decide where to put the three side lengths. The key is to start with \\(c\\), which is always on the side across from the right angle. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-c.png\" alt=\"\" width=\"200\" height=\"199.227\" class=\"aligncenter size-full wp-image-93526\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-c.png 745w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-c-300x300.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-c-150x150.png 150w\" sizes=\"(max-width: 745px) 100vw, 745px\" \/><\/p>\n<p>This is called the hypotenuse, and it\u2019s always the longest side.<\/p>\n<p>You may be asking yourself \u201cIf \\(c\\) is always across from the right angle, how do I tell which of the other two is \\(a\\) and which is \\(b\\)?\u201d It\u2019s a good question, and the answer is, it doesn\u2019t matter! Either of these two sides, which are called legs, can be used as \\(a\\) and then just use the other one for \\(b\\). Let\u2019s pick 3 cm for \\(a\\) and use 4 cm for \\(b\\). So this is what our theorem looks like when we have it filled in: \\(3^2+4^2=c^2\\)<\/p>\n<p>Now we just can evaluate 3 squared and 4 squared, which means multiplying 3 times 3 and 4 times 4 to get the following:<\/p>\n<div class=\"examplesentence\">\\(3 \\cdot 3=9\\hspace{30px}4\\cdot 4=16\\)<br \/>\n\\(9+16=c^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo, what is the final answer for \\(c^2\\)? A little addition tells us.<\/p>\n<div class=\"examplesentence\">\\(9+16=25\\)<br \/>\n\\(25=c^2\\) or \\(c^2=25\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow here\u2019s where it gets a little tricky. We now know that \\(c^2=25\\), but we want to know what \\(c\\) is, not what \\(c\\) squared is! So how can we get rid of that little 2? Well, we use the inverse, or opposite, operation of squaring something! And that inverse operation is the square root! Since it\u2019s an equation, whatever we do to one side of the equation we must do to the other, so I\u2019m going to take the square root of both sides. <\/p>\n<div class=\"examplesentence\">\\(\\sqrt{c^2}=\\sqrt{25}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe square root of \\(c^2\\) is \\(c\\) and the square root of 25 just happens to be 5. Look at that. It\u2019s always good to check our answer to see if it makes sense. <\/p>\n<h3><span id=\"Triangle_Inequality_Theorem\" class=\"m-toc-anchor\"><\/span>Triangle Inequality Theorem<\/h3>\n<p>\nSince we\u2019re finding \\(c\\), it should be longer than any of the other two sides, and 5 is greater than both 4 or 3. Also, because of the <strong>triangle inequality theorem<\/strong>, which is something we\u2019ll get to in a later video, the hypotenuse must be less than the sum of the other two sides, which means 5 has to be smaller than 3+4. Which, it is. <\/p>\n<h3><span id=\"Pythagorean_Triples\" class=\"m-toc-anchor\"><\/span>Pythagorean Triples<\/h3>\n<p>\nSo you might have noticed that the answer to this problem was a nice neat integer (5). This is actually kind of rare if we look at random triangles. But it\u2019s not rare in a math problem you might see on a test. It happens whenever a problem uses a <strong>Pythagorean triple<\/strong>. The triangle we just looked at is the most common kind, of a 3-4-5 right triangle. The legs measure 3 and 4 and the hypotenuse is 5. <\/p>\n<p>Sometimes it will be disguised by multiplying all the numbers by 2, which means we would get a (6-8-10) or multiplied by 10 which means we\u2019d have a (30-40-50) lengths or any other number. You don\u2019t need to know this to solve a Pythagorean theorem problem, but it\u2019s a nice shortcut to save you some time or allow you to check your answer another way. Other Pythagorean triples include 5-12-13, 8-15-17, and 7-24-25. There are many more, but these ones are the ones you\u2019ll see most often. <\/p>\n<h3><span id=\"Final_Example\" class=\"m-toc-anchor\"><\/span>Final Example<\/h3>\n<p>\nOf course, there are right triangles that aren\u2019t Pythagorean triples. Let\u2019s look at one just so we can see what the answer will look like. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-c75.png\" alt=\"\" width=\"250\" height=\"169.0546\" class=\"aligncenter size-full wp-image-93529\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-c75.png 760w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/right-triangle-with-square-c75-300x203.png 300w\" sizes=\"(max-width: 760px) 100vw, 760px\" \/><\/p>\n<p>Once again we\u2019re solving for the hypotenuse (the longest side, which is opposite the 90\u02da or right angle.) This is length \\(c\\). When we plug in 5 and 7 for \\(a\\) and \\(b\\) we get this: <\/p>\n<div class=\"examplesentence\">\\(5^2+7^2=c^2\\)<br \/>\n\\(2^5+4^9=c^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo let\u2019s add 25 + 49 to get \\(74=c^2\\).<\/p>\n<p>Then we take the square root of each side and find out that \\(c = \\sqrt{74}\\), now even though 74 isn\u2019t a perfect square. This <em>is<\/em> the answer. If you take the square root on a calculator you only get an approximation of the answer (which about 8.60232526&#8230;). We can use this approximation to do our checks: It\u2019s greater than either of the other two sides and it\u2019s less than the two sides added together. But when writing the answer we should use the square root form. <\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Pythagorean_Theorem_Practice_Problems\" class=\"m-toc-anchor\"><\/span>Pythagorean Theorem Practice Problems<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for the value of \\(c\\) in the right triangle below:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Pythagorean-Triangle-Example-1.svg\" alt=\"A right triangle with side lengths of 5 inches and 12 inches, and hypotenuse labeled as c.\" width=\"309.6\" height=\"164.8\" class=\"aligncenter size-full wp-image-287453\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">10 inches<\/div><div class=\"PQ\"  id=\"PQ-1-2\">11 inches<\/div><div class=\"PQ\"  id=\"PQ-1-3\">12 inches<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">13 inches<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The Pythagorean theorem states that \\(a^2+b^2=c^2\\), where \\(a\\) and \\(b\\) are the legs of the right triangle, and \\(c\\) is the hypotenuse.<\/p>\n<p>When the values for \\(a\\) and \\(b\\) are plugged into the equation, we have \\(5^2+12^2=c^2\\), which simplifies to \\(25+144=c^2\\). This then simplifies to \\(169=c^2\\).<\/p>\n<p>From here, find the square root of both sides of the equation. The square root of 169 is 13, and the square root of \\(c^2\\) is \\(c\\). Therefore, \\(c=13 \\mathrm{\\:in}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for the value of \\(c\\) in the right triangle below:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Pythagorean-Triangle-Example-2.svg\" alt=\"A right triangle with legs measuring 7 feet and 24 feet, and hypotenuse labeled c.\" width=\"309.6\" height=\"149.6\" class=\"aligncenter size-full wp-image-287456\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">25 feet<\/div><div class=\"PQ\"  id=\"PQ-2-2\">24 feet<\/div><div class=\"PQ\"  id=\"PQ-2-3\">28 feet<\/div><div class=\"PQ\"  id=\"PQ-2-4\">26 feet<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>When the values for \\(a\\) and \\(b\\) are plugged into the equation, we have \\(7^2+24^2=c^2\\), which simplifies to \\(49+576=c^2\\). This then simplifies to \\(625=c^2\\).<\/p>\n<p>From here, find the square root of both sides of the equation. The square root of 625 is 25, and the square root of \\(c^2\\) is \\(c\\). Therefore, \\(c=25 \\mathrm{\\: ft}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for the value of \\(c\\) in the right triangle below:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Pythagorean-Triangle-Example-3.svg\" alt=\"A right triangle with legs labeled 7 cm and 8 cm, and the hypotenuse labeled c.\" width=\"245.6\" height=\"164.8\" class=\"aligncenter size-full wp-image-287459\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(113 \\mathrm{\\:cm}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">\\(\\sqrt{113}\\mathrm{\\:cm}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(\\sqrt{64}\\mathrm{\\:cm}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(\\sqrt{49}\\mathrm{\\:cm}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>When the values for \\(a\\) and \\(b\\) are plugged into the equation, we have \\(7^2+8^2=c^2\\), which simplifies to \\(49+64=c^2\\). This then simplifies to \\(113=c^2\\).<\/p>\n<p>From here, find the square root of both sides of the equation. The square root of \\(c^2\\) is \\(c\\), but the square root of 113 is not a nice whole number, so we can leave it as \\(\\sqrt{113}\\). Therefore, \\(c=\\sqrt{113}\\mathrm{\\:cm}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich statement about the right triangle below is incorrect:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Pythagorean-Triangle-Example-4.svg\" alt=\"A right triangle with side lengths 3 and 4, and hypotenuse labeled c. The right angle is between the two shorter sides.\" width=\"210.4\" height=\"164.8\" class=\"aligncenter size-full wp-image-287450\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">The hypotenuse of 5<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(c\\) will be larger than \\(a\\) and \\(b\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">The hypotenuse if 4<\/div><div class=\"PQ\"  id=\"PQ-4-4\">3 and 4 represent \\(a\\) and \\(b\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Choice A is correct because the Pythagorean theorem can be applied to solve for \\(c\\).<\/p>\n<p>Choice B is correct because the hypotenuse (\\(c\\)) will always be the longest side of a right triangle.<\/p>\n<p>Choice D is also correct because \\(a\\) and \\(b\\) are defined as the two legs of a right triangle that come together to form the 90-degree angle.<\/p>\n<p>Therefore, only Choice C is incorrect.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich right triangle lengths show incorrect values for \\(a\\), \\(b\\), and \\(c\\) according to the Pythagorean theorem?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">Triangle A: \\(a=8, b=15, c=17\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">Triangle B: \\(a=3, b=4, c=5\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">Triangle C: \\(a=8, b=9, c=10\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">Triangle D: \\(a=6, b=8, c=10\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The Pythagorean theorem can be used to prove that the lengths of Choice C are incorrect.<\/p>\n<p>If 8 is plugged in for \\(a\\), 9 is plugged in for \\(b\\), and 10 is plugged in for \\(c\\),  the result is \\(8^2+9^2=10^2\\). Simplifying each side of the equation shows that the two sides are not equal. 145 does not equal 100.<\/p>\n<p>Therefore, triangle C is incorrect.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<div class=\"spoiler\" id=\"worksheets-spoiler\">\n<h2 style=\"text-align:center;\"><span id=\"Pythagorean_Theorem_Worksheets\" class=\"m-toc-anchor\"><\/span>Pythagorean Theorem Worksheets<\/h2>\n<div style=\"display: flex;flex-flow: row wrap;justify-content: center;\">\n<p style=\"width:100%;\">Use our free printable Pythagorean Theorem worksheets for additional practice!<\/p>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Pythagorean Theorem Worksheet<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/12\/Pythagorean-Theorem-Worksheets.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/12\/Pythagorean-worksheet-preview.png\" alt=\"Pythagorean Theorem Worksheet Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<div style=\"text-align:center;max-width:300px;margin:15px;\">\n\t\t\t\t\t\t<strong>Pythagorean Theorem (Answer Key)<\/strong><br \/>\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/12\/Pythagorean-Theorem-Answer-Sheets-1.pdf\"><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/12\/Pythagorean-Theorem-Worksheet-Answer-Key-preview-image.png\" alt=\"Pythagorean Theorem (Answer Key) Worksheet Preview\" style=\"box-shadow: 1.5px 1.5px 5px grey;\"><br \/>\n\t\t\t\t\t\t\t<button class=\"buttonmltpctn\" style=\"width: 90%;color: black;font-size: 0.9em;\" data-uw-styling-context=\"true\">CLICK HERE TO DOWNLOAD<\/button><br \/>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":99727,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4531","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-triangle-videos","8":"page_type-video","9":"content_type-practice-questions","10":"content_type-worksheets","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=4531"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4531\/revisions"}],"predecessor-version":[{"id":287489,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4531\/revisions\/287489"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/99727"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}