{"id":1869,"date":"2026-03-25T10:22:36","date_gmt":"2026-03-25T10:22:36","guid":{"rendered":"https:\/\/blog.think10x.ai\/?p=1869"},"modified":"2026-04-08T16:33:32","modified_gmt":"2026-04-08T16:33:32","slug":"pythagorean-theorem-explained","status":"publish","type":"post","link":"https:\/\/www.think10x.ai\/blog\/pythagorean-theorem-explained\/","title":{"rendered":"The Pythagorean Theorem: Complete Guide (a\u00b2 + b\u00b2 = c\u00b2)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1869\" class=\"elementor elementor-1869\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-435058a e-flex e-con-boxed e-con e-parent\" data-id=\"435058a\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0fccce0 elementor-widget elementor-widget-text-editor\" data-id=\"0fccce0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>The <strong>Pythagorean theorem<\/strong> applies to every right triangle. It connects the three sides through one equation. Once you understand it, you can find missing sides, classify triangles, calculate diagonals, and solve coordinate distances using the same rule.<\/p>\n<h2>The Pythagorean Theorem Explained<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e292363 elementor-widget elementor-widget-video\" data-id=\"e292363\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/jiJeKSbfqOM?si=e4PkDT1zGLwxMJdj&amp;t=17&quot;,&quot;start&quot;:17,&quot;end&quot;:95,&quot;cc_load_policy&quot;:&quot;yes&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4d5b5cf elementor-widget elementor-widget-text-editor\" data-id=\"4d5b5cf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h2>When Do You Add and When Do You Subtract?<\/h2>\n<p>Decide which case applies before writing any equation.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fb28a30 eael-table-align-center eael-dt-th-align-left elementor-widget elementor-widget-eael-data-table\" data-id=\"fb28a30\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"eael-data-table.default\">\n\t\t\t\t\t\t\t<div class=\"eael-data-table-wrap\" data-table_id=\"fb28a30\" id=\"eael-data-table-wrapper-fb28a30\" data-custom_responsive=\"false\">\n\t\t\t<table class=\"tablesorter eael-data-table center\" id=\"eael-data-table-fb28a30\">\n\t\t\t    <thead>\n\t\t\t        <tr class=\"table-header\">\n\t\t\t\t\t\t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">Situation<\/span><\/th>\n\t\t\t        \t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">Table Header<\/span><\/th>\n\t\t\t        \t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">Table Header<\/span><\/th>\n\t\t\t        \t\t\t\t        <\/tr>\n\t\t\t    <\/thead>\n\t\t\t  \t<tbody>\n\t\t\t\t\t\t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tBoth legs known, find hypotenuse\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tc = \u221a(a\u00b2 + b\u00b2)\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tAdd the squares\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tHypotenuse and one leg known, find a leg\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\ta = \u221a(c\u00b2 \u2212 b\u00b2)\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tSubtract the squares\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tThree sides given, classify the triangle\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tCompare a\u00b2 + b\u00b2 with c\u00b2\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tAdd, then compare\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t    <\/tbody>\n\t\t\t<\/table>\n\t\t<\/div>\n\t  \t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9c0bdfe e-flex e-con-boxed e-con e-parent\" data-id=\"9c0bdfe\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a4b6954 elementor-widget elementor-widget-text-editor\" data-id=\"a4b6954\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h2>What Does the Pythagorean Theorem Actually Mean?<\/h2>\n<p>The theorem is a statement about area. If you draw a square on each side of a right triangle, the combined area of the two smaller squares equals the area of the square on the hypotenuse.<\/p>\n<p>3\u00b2 + 4\u00b2 = 5\u00b2<\/p>\n<p>9 + 16 = 25<\/p>\n<p>LHS = RHS<\/p>\n<p>The two legs,\u00a0<strong>a<\/strong>\u00a0and\u00a0<strong>b<\/strong>, meet at the right angle. The hypotenuse\u00a0<strong>c<\/strong>\u00a0is opposite the right angle and is always the longest side. Every formula in this topic begins by identifying\u00a0<em>c<\/em>\u00a0correctly.<\/p>\n<h2>How Do You Find the Hypotenuse?<\/h2>\n<p><span style=\"font-weight: 400;\">To find the hypotenuse, square both legs (a , b), add them, and take the square root. The hypotenuse (c) is always the longest side.<\/span><\/p>\n<h3>Example 1. Whole-number answer<\/h3>\n<ul>\n<li>Legs &#8211; 3 and 4<\/li>\n<li>c\u00b2 = 3\u00b2 + 4\u00b2 = 9 + 16 = 25<\/li>\n<li>c = \u221a25 = <strong>5<\/strong><\/li>\n<\/ul>\n<h3>Example 2. Irrational answer<\/h3>\n<ul>\n<li>Legs &#8211; 5 and 7<\/li>\n<li>c\u00b2 = 5\u00b2 + 7\u00b2 = 25 + 49 = 74<\/li>\n<li>c = <strong>\u221a74<\/strong><\/li>\n<\/ul>\n<p>Since 74 is not a perfect square, leave the answer as \u221a74 unless the problem asks for a decimal.<\/p>\n<h3>Example 3. Scaled triple<\/h3>\n<ul>\n<li>Legs &#8211; 9 and 12<\/li>\n<li>c\u00b2 = 9\u00b2 + 12\u00b2 = 81 + 144 = 225<\/li>\n<li>c = \u221a225 = <strong>15<\/strong><\/li>\n<\/ul>\n<p>9 and 12 both divide by 3 to give 3 and 4, which is the 3-4-5 triple. The hypotenuse is 5 \u00d7 3 = 15. No full calculation needed.<\/p>\n<div class=\"flex flex-col text-sm pb-25\">\n<section class=\"text-token-text-primary w-full focus:outline-none [--shadow-height:45px] has-data-writing-block:pointer-events-none has-data-writing-block:-mt-(--shadow-height) has-data-writing-block:pt-(--shadow-height) [&amp;:has([data-writing-block])&gt;*]:pointer-events-auto scroll-mt-[calc(var(--header-height)+min(200px,max(70px,20svh)))]\" dir=\"auto\" data-turn-id=\"request-WEB:216a05ee-e585-440c-abaa-1ca6f3ed4480-8\" data-testid=\"conversation-turn-4\" data-scroll-anchor=\"true\" data-turn=\"assistant\">\n<div class=\"text-base my-auto mx-auto pb-10 [--thread-content-margin:var(--thread-content-margin-xs,calc(var(--spacing)*4))] @w-sm\/main:[--thread-content-margin:var(--thread-content-margin-sm,calc(var(--spacing)*6))] @w-lg\/main:[--thread-content-margin:var(--thread-content-margin-lg,calc(var(--spacing)*16))] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:40rem] @w-lg\/main:[--thread-content-max-width:48rem] mx-auto max-w-(--thread-content-max-width) flex-1 group\/turn-messages focus-visible:outline-hidden relative flex w-full min-w-0 flex-col agent-turn\">\n<div class=\"flex max-w-full flex-col gap-4 grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal outline-none keyboard-focused:focus-ring [.text-message+&amp;]:mt-1\" dir=\"auto\" tabindex=\"0\" data-message-author-role=\"assistant\" data-message-id=\"7343085e-82db-4f99-a9e2-60af3f92aedc\" data-message-model-slug=\"gpt-5-3\" data-turn-start-message=\"true\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden\">\n<div class=\"markdown prose dark:prose-invert w-full wrap-break-word dark markdown-new-styling\">\n<h2 data-section-id=\"1h5pifi\" data-start=\"0\" data-end=\"65\" data-is-last-node=\"\" data-is-only-node=\"\">Ladder Against a Wall Pythagorean Theorem Example<\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<h3>Question<\/h3>\n<p>A ladder leans against a wall and reaches the upper right corner of a window 12 feet above the ground. The window is 9 feet wide and the base of the ladder sits directly below the window&#8217;s left edge. How long is the ladder?<\/p>\n<h3>Answer choices<\/h3>\n<p>A. 12 \u00a0 B. 13 \u00a0 C. 15 \u00a0 D. 21<\/p>\n<h3>Solution<\/h3>\n<ul>\n<li>Vertical leg = <strong>12 ft<\/strong>, Horizontal leg = <strong>9 ft<\/strong>, Ladder = <strong>hypotenuse<\/strong><\/li>\n<li>L\u00b2 = 9\u00b2 + 12\u00b2 = 81 + 144 = 225<\/li>\n<li>L = \u221a225 = 15 ft<\/li>\n<\/ul>\n<h3>Triple shortcut<\/h3>\n<p>9 \u00f7 3 = 3 and 12 \u00f7 3 = 4, matching the 3-4-5 triple scaled by 3. The hypotenuse is 5 \u00d7 3 = 15 instantly.<\/p>\n<h3>Why the other choices are wrong<\/h3>\n<p><strong>A<\/strong> (12) mistakes a leg for the hypotenuse, <strong>B<\/strong> (13) incorrectly applies the 5-12-13 triple and <strong>D<\/strong> (21) adds the legs directly without squaring.<\/p>\n<h2>Think10x.ai Video Explaining the Ladder Problem<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7a3669c elementor-widget elementor-widget-video\" data-id=\"7a3669c\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/jiJeKSbfqOM?si=0hp6ifl5OD2cY3sB&quot;,&quot;start&quot;:218,&quot;end&quot;:332,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-98bad5e elementor-widget elementor-widget-text-editor\" data-id=\"98bad5e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h2>How Do You Find a Missing Leg?<\/h2><p>Subtract the square of the known leg from the square of the hypotenuse, then take the square root.<\/p><ul><li>Hypotenuse &#8211; 13<\/li><li>Known leg &#8211; 5<\/li><li>a\u00b2 = 13\u00b2 \u2212 5\u00b2 = 169 \u2212 25 = 144<\/li><li>a = \u221a144 = 12<\/li><\/ul><p>If the result comes out longer than the hypotenuse, the setup is wrong. Check which side is actually the hypotenuse before substituting.<\/p><h2>Missing Leg Worked Example and Solution<\/h2><h3>Question<\/h3><p>A right triangle has a hypotenuse of 13\u221a2 and one leg of 11. Find the length of the other leg.<\/p><h3>Answer choices<\/h3><p>A. \u221a217 \u00a0 B. \u221a219 \u00a0 C. 15 \u00a0 D. 13<\/p><h3>Solution<\/h3><ul><li>Write the missing-leg formula (a\u00b2 = c\u00b2 \u2212 b\u00b2)<\/li><li>Square the radical hypotenuse &#8211; (13\u221a2)\u00b2 = 13\u00b2 \u00d7 (\u221a2)\u00b2 = 169 \u00d7 2 = 338<\/li><li>Square the known leg &#8211; 11\u00b2 = 121<\/li><li>Subtract and solve &#8211; a\u00b2 = 338 \u2212 121 = 217<\/li><li>a = <strong>\u221a217<\/strong><\/li><\/ul><h3>Key rule<\/h3><p>When the hypotenuse is written as n\u221ak, square both parts separately &#8211; (n\u221ak)\u00b2 = n\u00b2 \u00b7 k. Squaring only the coefficient 13 and ignoring \u221a2 is the most common error on this type of question.<\/p><h3>Why the other choices are wrong<\/h3><p><strong>B<\/strong> (\u221a219) comes from a slip when squaring 11, <strong>C<\/strong> (15) forces a familiar triple and ignores the radical and <strong>D<\/strong> (13) squares only the coefficient.<\/p><h2>Think10x.ai Video Explaining Missing Leg Problem<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a4205c elementor-widget elementor-widget-video\" data-id=\"6a4205c\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/jiJeKSbfqOM?si=0hp6ifl5OD2cY3sB&quot;,&quot;start&quot;:95,&quot;end&quot;:216,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-97d9410 elementor-widget elementor-widget-text-editor\" data-id=\"97d9410\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h2>What Are Pythagorean Triples?<\/h2>\n<p>A Pythagorean triple is a set of three positive integers that satisfy a\u00b2 + b\u00b2 = c\u00b2. Recognizing one in a problem means you can state the answer immediately, without any calculation.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4cd0dd7 eael-table-align-center eael-dt-th-align-left elementor-widget elementor-widget-eael-data-table\" data-id=\"4cd0dd7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"eael-data-table.default\">\n\t\t\t\t\t\t\t<div class=\"eael-data-table-wrap\" data-table_id=\"4cd0dd7\" id=\"eael-data-table-wrapper-4cd0dd7\" data-custom_responsive=\"false\">\n\t\t\t<table class=\"tablesorter eael-data-table center\" id=\"eael-data-table-4cd0dd7\">\n\t\t\t    <thead>\n\t\t\t        <tr class=\"table-header\">\n\t\t\t\t\t\t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">a<\/span><\/th>\n\t\t\t        \t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">b<\/span><\/th>\n\t\t\t        \t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">c<\/span><\/th>\n\t\t\t        \t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">Notes<\/span><\/th>\n\t\t\t        \t\t\t\t        <\/tr>\n\t\t\t    <\/thead>\n\t\t\t  \t<tbody>\n\t\t\t\t\t\t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t3\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t4\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t5\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tMost common\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t5\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t12\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t13\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tCommon on tests\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t8\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t15\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t17\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tHarder word problems\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t7\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t24\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t25\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tUseful extra triple\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t6\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t8\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t10\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t3 &#8211; 4 &#8211; 5 \u00d7 2\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t9\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t12\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t15\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t3 &#8211; 4 &#8211; 5 \u00d7 3\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t10\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t24\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t26\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t5 &#8211; 12 &#8211; 13 \u00d7 2\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t15\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t20\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t25\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t3 &#8211; 4 &#8211; 5 \u00d7 5\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t    <\/tbody>\n\t\t\t<\/table>\n\t\t<\/div>\n\t  \t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1cfd225 elementor-widget elementor-widget-text-editor\" data-id=\"1cfd225\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h3>Scale-factor shortcut<\/h3>\n<p>\u00a0If both legs divide by the same number to match a known triple, multiply the third side by that same factor.<\/p>\n<h2>How Do You Use the Converse to Classify a Triangle?<\/h2>\n<p><span style=\"font-weight: 400;\">The converse helps you decide whether a triangle is <strong>right<\/strong>, <strong>acute<\/strong>, or <strong>obtuse<\/strong>. Always identify the longest side first and label it as c before applying the test.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2858b80 eael-table-align-center eael-dt-th-align-left elementor-widget elementor-widget-eael-data-table\" data-id=\"2858b80\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"eael-data-table.default\">\n\t\t\t\t\t\t\t<div class=\"eael-data-table-wrap\" data-table_id=\"2858b80\" id=\"eael-data-table-wrapper-2858b80\" data-custom_responsive=\"false\">\n\t\t\t<table class=\"tablesorter eael-data-table center\" id=\"eael-data-table-2858b80\">\n\t\t\t    <thead>\n\t\t\t        <tr class=\"table-header\">\n\t\t\t\t\t\t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">If<\/span><\/th>\n\t\t\t        \t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">Then the triangle is<\/span><\/th>\n\t\t\t        \t\t\t\t        <\/tr>\n\t\t\t    <\/thead>\n\t\t\t  \t<tbody>\n\t\t\t\t\t\t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\ta\u00b2 + b\u00b2 = c\u00b2\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tRight\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\ta\u00b2 + b\u00b2 &gt; c\u00b2\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tAcute\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\ta\u00b2 + b\u00b2 &lt; c\u00b2\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tObtuse\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t    <\/tbody>\n\t\t\t<\/table>\n\t\t<\/div>\n\t  \t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5959381 elementor-widget elementor-widget-text-editor\" data-id=\"5959381\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h3>Worked example<\/h3>\n<ul>\n<li><span style=\"font-weight: 400;\">Sides &#8211; <strong>7, 24, 25<\/strong>. <\/span><\/li>\n<li><span style=\"font-weight: 400;\">Since 25 is the longest side, let c = 25.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">7\u00b2 + 24\u00b2 = 49 + 576 = 625 <\/span><\/li>\n<li><span style=\"font-weight: 400;\">25\u00b2 = 625<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Because both sides are equal, this is a <strong>right triangle.<\/strong><\/span><\/p>\n<h2>How Do You Find the Diagonal of a Rectangle?<\/h2>\n<p>A diagonal divides a rectangle into two right triangles. The <strong>two side lengths<\/strong> are the legs and the <strong>diagonal<\/strong> is the hypotenuse.<\/p>\n<p>d = \u221a(l\u00b2 + w\u00b2)<\/p>\n<h3>Example 1. Room Diagonal<\/h3>\n<p>Length is 15 ft and width is 20 ft<\/p>\n<ul>\n<li>d\u00b2 = 15\u00b2 + 20\u00b2 = 225 + 400 = 625<\/li>\n<li>d = \u221a625 = 25 ft<\/li>\n<\/ul>\n<p>15 and 20 are the <strong>3-4-5 triple<\/strong> multiplied by 5, so the diagonal is 5 \u00d7 5 = 25 immediately.<\/p>\n<h3>Example 2. Screen Diagonal<\/h3>\n<p>Width is 48 in and height is 27 in<\/p>\n<ul>\n<li>d\u00b2 = 48\u00b2 + 27\u00b2 = 2,304 + 729 = 3,033<\/li>\n<li>d = \u221a3,033 = 55.1 in<\/li>\n<\/ul>\n<p><strong>Screen sizes<\/strong> (TVs, monitors, tablets, phones) are always measured diagonally using this formula.<\/p>\n<h2>Where Is the Pythagorean Theorem Used in Real Life?<\/h2>\n<h3>1. Ladders and ramps<\/h3>\n<p>The <strong>foot-to-wall<\/strong> distance and the height reached are the two legs; the ladder is the hypotenuse.<\/p>\n<p>Ladder reaches 16 ft up a wall<\/p>\n<p>Base is 12 ft from wall<\/p>\n<ul>\n<li>L\u00b2 = 12\u00b2 + 16\u00b2 = 144 + 256 = 400<\/li>\n<li>L = \u221a400 = 20 ft<\/li>\n<\/ul>\n<h3>2. Construction (Checking Right Angles)<\/h3>\n<p>Builders use the 3-4-5 rule to verify a 90\u00b0 corner. Mark 3 ft along one wall and 4 ft along the adjacent wall. If the diagonal is 5 ft, the corner is a perfect right angle. The same check works at any scale: 6-8-10, 9-12-15, and so on.<\/p>\n<h3>3. Distance on a coordinate grid<\/h3>\n<p>The <strong>horizontal<\/strong> and <strong>vertical<\/strong> differences between two points are the legs. The straight-line distance is the hypotenuse.<\/p>\n<ul>\n<li>d = \u221a((x\u2082 \u2212 x\u2081)\u00b2 + (y\u2082 \u2212 y\u2081)\u00b2)<\/li>\n<li>Points (1, 2) and (7, 10)<\/li>\n<li>Horizontal &#8211; 7 \u2212 1 = 6<\/li>\n<li>Vertical &#8211; 10 \u2212 2 = 8<\/li>\n<li>d = \u221a(36 + 64)<\/li>\n<li>\u221a100 = 10<\/li>\n<\/ul>\n<h2>Common Traps and How to Avoid Them<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-38c723a e-flex e-con-boxed e-con e-parent\" data-id=\"38c723a\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5e0b900 eael-table-align-center eael-dt-th-align-left elementor-widget elementor-widget-eael-data-table\" data-id=\"5e0b900\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"eael-data-table.default\">\n\t\t\t\t\t\t\t<div class=\"eael-data-table-wrap\" data-table_id=\"5e0b900\" id=\"eael-data-table-wrapper-5e0b900\" data-custom_responsive=\"false\">\n\t\t\t<table class=\"tablesorter eael-data-table center\" id=\"eael-data-table-5e0b900\">\n\t\t\t    <thead>\n\t\t\t        <tr class=\"table-header\">\n\t\t\t\t\t\t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">Trap<\/span><\/th>\n\t\t\t        \t\t\t\t            <th class=\"\" id=\"\" colspan=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"data-table-header-text\">Fix<\/span><\/th>\n\t\t\t        \t\t\t\t        <\/tr>\n\t\t\t    <\/thead>\n\t\t\t  \t<tbody>\n\t\t\t\t\t\t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tAdding legs before squaring\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tSquare first, then add\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tForgetting the square root\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tAlways take the square root at the end\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tSubtracting to find the hypotenuse\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tOnly subtract when finding a missing leg\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tMislabeling the hypotenuse\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tIt is opposite the right angle, always the longest side, and the side you assign as c in all formulas\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tSquaring a radical incorrectly\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tSquare both parts separately: (n\u221ak)\u00b2 = n\u00b2k\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tRounding too early\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t   \t\t\t\t\t\t\t\t\t\t\t<td colspan=\"\" rowspan=\"\" class=\"\" id=\"\">\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"td-content-wrapper\"><div class=\"td-content\">\n\t\t\t\t\t\t\t\t\t\t\t\t\tRound only at the final step\t\t\t\t\t\t\t\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/td>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/tr>\n\t\t\t        \t\t\t    <\/tbody>\n\t\t\t<\/table>\n\t\t<\/div>\n\t  \t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f31a61e elementor-widget elementor-widget-text-editor\" data-id=\"f31a61e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h2>Frequently Asked Questions<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e104126 elementor-widget elementor-widget-eael-adv-accordion\" data-id=\"e104126\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"eael-adv-accordion.default\">\n\t\t\t\t\t            <div class=\"eael-adv-accordion\" id=\"eael-adv-accordion-e104126\" data-scroll-on-click=\"no\" data-scroll-speed=\"300\" data-accordion-id=\"e104126\" data-accordion-type=\"accordion\" data-toogle-speed=\"300\">\n            <div class=\"eael-accordion-list\">\n\t\t\t\t\t<div id=\"what-is-the-pythagorean-theorem\" class=\"elementor-tab-title eael-accordion-header\" tabindex=\"0\" data-tab=\"1\" aria-controls=\"elementor-tab-content-2351\"><span class=\"eael-advanced-accordion-icon-closed\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-advanced-accordion-icon-opened\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-accordion-tab-title\">What is the Pythagorean theorem?<\/span><svg aria-hidden=\"true\" class=\"fa-toggle e-font-icon-svg e-fas-angle-right\" viewBox=\"0 0 256 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z\"><\/path><\/svg><\/div><div id=\"elementor-tab-content-2351\" class=\"eael-accordion-content clearfix\" data-tab=\"1\" aria-labelledby=\"what-is-the-pythagorean-theorem\"><p>It states that in any right triangle, a\u00b2 + b\u00b2 = c\u00b2, where a and b are the legs and c is the hypotenuse. It only applies to right triangles.<\/p><\/div>\n\t\t\t\t\t<\/div><div class=\"eael-accordion-list\">\n\t\t\t\t\t<div id=\"how-do-you-find-a-missing-leg\" class=\"elementor-tab-title eael-accordion-header\" tabindex=\"0\" data-tab=\"2\" aria-controls=\"elementor-tab-content-2352\"><span class=\"eael-advanced-accordion-icon-closed\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-advanced-accordion-icon-opened\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-accordion-tab-title\">How do you find a missing leg?<\/span><svg aria-hidden=\"true\" class=\"fa-toggle e-font-icon-svg e-fas-angle-right\" viewBox=\"0 0 256 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z\"><\/path><\/svg><\/div><div id=\"elementor-tab-content-2352\" class=\"eael-accordion-content clearfix\" data-tab=\"2\" aria-labelledby=\"how-do-you-find-a-missing-leg\"><p>Use a = \u221a(c\u00b2 \u2212 b\u00b2). Square the hypotenuse, subtract the square of the known leg, then take the square root. Confirm which side is the hypotenuse before substituting.<\/p><\/div>\n\t\t\t\t\t<\/div><div class=\"eael-accordion-list\">\n\t\t\t\t\t<div id=\"what-pythagorean-triples-should-i-know\" class=\"elementor-tab-title eael-accordion-header\" tabindex=\"0\" data-tab=\"3\" aria-controls=\"elementor-tab-content-2353\"><span class=\"eael-advanced-accordion-icon-closed\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-advanced-accordion-icon-opened\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-accordion-tab-title\">What Pythagorean triples should I know?<\/span><svg aria-hidden=\"true\" class=\"fa-toggle e-font-icon-svg e-fas-angle-right\" viewBox=\"0 0 256 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z\"><\/path><\/svg><\/div><div id=\"elementor-tab-content-2353\" class=\"eael-accordion-content clearfix\" data-tab=\"3\" aria-labelledby=\"what-pythagorean-triples-should-i-know\"><p>Start with 3-4-5 and 5-12-13. Then add 8-15-17 and 7-24-25. Any multiple of a triple is also a triple: 6-8-10, 9-12-15, 10-24-26, and so on.<\/p><\/div>\n\t\t\t\t\t<\/div><div class=\"eael-accordion-list\">\n\t\t\t\t\t<div id=\"how-do-you-find-the-diagonal-of-a-rectangle\" class=\"elementor-tab-title eael-accordion-header\" tabindex=\"0\" data-tab=\"4\" aria-controls=\"elementor-tab-content-2354\"><span class=\"eael-advanced-accordion-icon-closed\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-advanced-accordion-icon-opened\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-accordion-tab-title\">How do you find the diagonal of a rectangle?<\/span><svg aria-hidden=\"true\" class=\"fa-toggle e-font-icon-svg e-fas-angle-right\" viewBox=\"0 0 256 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z\"><\/path><\/svg><\/div><div id=\"elementor-tab-content-2354\" class=\"eael-accordion-content clearfix\" data-tab=\"4\" aria-labelledby=\"how-do-you-find-the-diagonal-of-a-rectangle\"><p>Use d = \u221a(l\u00b2 + w\u00b2). Square the length and width, add them, then take the square root. This is the same structure as finding the hypotenuse of a right triangle.<\/p><\/div>\n\t\t\t\t\t<\/div><div class=\"eael-accordion-list\">\n\t\t\t\t\t<div id=\"how-do-you-square-a-radical-hypotenuse-like-132\" class=\"elementor-tab-title eael-accordion-header\" tabindex=\"0\" data-tab=\"5\" aria-controls=\"elementor-tab-content-2355\"><span class=\"eael-advanced-accordion-icon-closed\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-advanced-accordion-icon-opened\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-accordion-tab-title\">How do you square a radical hypotenuse like 13\u221a2?<\/span><svg aria-hidden=\"true\" class=\"fa-toggle e-font-icon-svg e-fas-angle-right\" viewBox=\"0 0 256 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z\"><\/path><\/svg><\/div><div id=\"elementor-tab-content-2355\" class=\"eael-accordion-content clearfix\" data-tab=\"5\" aria-labelledby=\"how-do-you-square-a-radical-hypotenuse-like-132\"><p>Square both parts separately. (13\u221a2)\u00b2 = 13\u00b2 \u00d7 (\u221a2)\u00b2 = 169 \u00d7 2 = 338. Squaring only the coefficient and ignoring the radical is the most common error.<\/p><\/div>\n\t\t\t\t\t<\/div><div class=\"eael-accordion-list\">\n\t\t\t\t\t<div id=\"what-is-the-distance-formula-and-how-does-it-relate-to-the-theorem\" class=\"elementor-tab-title eael-accordion-header\" tabindex=\"0\" data-tab=\"6\" aria-controls=\"elementor-tab-content-2356\"><span class=\"eael-advanced-accordion-icon-closed\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-advanced-accordion-icon-opened\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-accordion-tab-title\">What is the distance formula and how does it relate to the theorem?<\/span><svg aria-hidden=\"true\" class=\"fa-toggle e-font-icon-svg e-fas-angle-right\" viewBox=\"0 0 256 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z\"><\/path><\/svg><\/div><div id=\"elementor-tab-content-2356\" class=\"eael-accordion-content clearfix\" data-tab=\"6\" aria-labelledby=\"what-is-the-distance-formula-and-how-does-it-relate-to-the-theorem\"><p>The distance formula d = \u221a((x\u2082 \u2212 x\u2081)\u00b2 + (y\u2082 \u2212 y\u2081)\u00b2) is the Pythagorean theorem applied to coordinate geometry. The horizontal and vertical differences are the legs; the straight-line distance is the hypotenuse.<\/p><\/div>\n\t\t\t\t\t<\/div><div class=\"eael-accordion-list\">\n\t\t\t\t\t<div id=\"when-does-the-pythogorean-theorem-not-apply\" class=\"elementor-tab-title eael-accordion-header\" tabindex=\"0\" data-tab=\"7\" aria-controls=\"elementor-tab-content-2357\"><span class=\"eael-advanced-accordion-icon-closed\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-advanced-accordion-icon-opened\"><svg aria-hidden=\"true\" class=\"fa-accordion-icon e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span><span class=\"eael-accordion-tab-title\">When does the Pythogorean theorem not apply?<\/span><svg aria-hidden=\"true\" class=\"fa-toggle e-font-icon-svg e-fas-angle-right\" viewBox=\"0 0 256 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z\"><\/path><\/svg><\/div><div id=\"elementor-tab-content-2357\" class=\"eael-accordion-content clearfix\" data-tab=\"7\" aria-labelledby=\"when-does-the-pythogorean-theorem-not-apply\"><p>It only applies to right triangles. For triangles without a right angle, use the Law of Cosines or Law of Sines instead.<\/p><\/div>\n\t\t\t\t\t<\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c7e632f e-flex e-con-boxed e-con e-parent\" data-id=\"c7e632f\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5a7782e elementor-widget elementor-widget-text-editor\" data-id=\"5a7782e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h2>Need Help With Your Own Question?<\/h2><p><span style=\"font-weight: 400;\">Upload a<\/span><a href=\"https:\/\/www.think10x.ai\/take-a-clear-photo-of-a-question\/\"> <span style=\"font-weight: 400;\">clear photo<\/span><\/a><span style=\"font-weight: 400;\"> to Think10x.ai and get an instant video explanation. Built for <a href=\"https:\/\/mentomind.ai\/\" rel=\"noopener\">tutors<\/a> and <a href=\"https:\/\/mentomind.ai\/for-students\/\" rel=\"noopener\">students<\/a>. Private by default.<\/span><\/p><p><span style=\"font-weight: 400;\"><strong><a href=\"https:\/\/www.think10x.ai\/\">Try <\/a><\/strong><\/span><a href=\"https:\/\/www.think10x.ai\/create\/\"><b>Think10x.ai<\/b><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The Pythagorean theorem applies to every right triangle. It connects the three sides through one equation. Once you understand it, you can find missing sides, classify triangles, calculate diagonals, and solve coordinate distances using the same rule. The Pythagorean Theorem Explained https:\/\/youtu.be\/jiJeKSbfqOM?si=e4PkDT1zGLwxMJdj&#038;t=17 When Do You Add and When Do You Subtract? Decide which case applies [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":1983,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/media.mentomind.ai\/img\/t10x\/bp\/The_Pythagorean_Theorem_Complete_Guide.webp","fifu_image_alt":"Visual guide to questions on Pythagorean theorem showing right triangle with sides a, b and hypotenuse c","footnotes":""},"categories":[8,1],"tags":[],"class_list":["post-1869","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blogs","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/posts\/1869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/comments?post=1869"}],"version-history":[{"count":6,"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/posts\/1869\/revisions"}],"predecessor-version":[{"id":1984,"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/posts\/1869\/revisions\/1984"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/media\/1983"}],"wp:attachment":[{"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/media?parent=1869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/categories?post=1869"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.think10x.ai\/blog\/wp-json\/wp\/v2\/tags?post=1869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}