{"id":58895,"date":"2020-04-24T18:17:20","date_gmt":"2020-04-24T18:17:20","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=58895"},"modified":"2026-03-25T15:15:24","modified_gmt":"2026-03-25T20:15:24","slug":"general-rules-of-triangles","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/general-rules-of-triangles\/","title":{"rendered":"General Rules for Triangles"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_WXcfwfmGOVQ\" 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_WXcfwfmGOVQ\" data-source-videoID=\"WXcfwfmGOVQ\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"General Rules for Triangles Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"General Rules for Triangles\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_WXcfwfmGOVQ:hover {cursor:pointer;} img#videoThumbnailImage_WXcfwfmGOVQ {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/07\/updated-general-rules-for-triangles-64bec5d127991.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_WXcfwfmGOVQ\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_WXcfwfmGOVQ\" 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\",\"General Rules for Triangles\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_WXcfwfmGOVQ\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_WXcfwfmGOVQ\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_WXcfwfmGOVQ\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction bqz_Function() {\n  var x = document.getElementById(\"bqz\");\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=\"bqz_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=\"bqz\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Triangle_Inequality_Theorem\" class=\"smooth-scroll\">Triangle Inequality Theorem<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Angle_Sum_Property\" class=\"smooth-scroll\">Angle Sum Property<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Isosceles_Triangle_Theorem\" class=\"smooth-scroll\">Isosceles Triangle Theorem<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Midsegment_Theorem\" class=\"smooth-scroll\">Midsegment Theorem<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Triangle_Practice_Questions\" class=\"smooth-scroll\">Triangle Practice Questions<\/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>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on the general rules of triangles.<\/p>\n<p>Today, we\u2019re going to look at the four most important properties of triangles.<\/p>\n<h2><span id=\"Triangle_Inequality_Theorem\" class=\"m-toc-anchor\"><\/span>Triangle Inequality Theorem<\/h2>\n<p>\nThe first property is known as the triangle inequality theorem. It states that no side of a triangle can be longer than the other two sides added together.<\/p>\n<p>Let\u2019s look at this triangle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65083\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-inequality-theorem.png\" alt=\"triangle inequality theorem\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-inequality-theorem.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-inequality-theorem-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-inequality-theorem-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-inequality-theorem-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-inequality-theorem-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<p>As you can see, one of the sides is a lot longer than each of the other two sides. But when we measure the sides, the length of the smaller sides added together is still longer than the length of the longer side.<\/p>\n<p>If I pushed the top of this triangle lower, the sides would get a bit shorter but they\u2019d still add up to a little more than 15. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65080\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/shorter-sides.png\" alt=\"triangle with shorter sides\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/shorter-sides.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/shorter-sides-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/shorter-sides-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/shorter-sides-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/shorter-sides-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<p>If I flattened them completely so that they\u2019d form a straight line segment they would add up to 15, but then we wouldn\u2019t have a triangle anymore.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65089\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/flat-lines.png\" alt=\"flat lines\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/flat-lines.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/flat-lines-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/flat-lines-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/flat-lines-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/flat-lines-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<p>Feel free to try it yourself. Cut a few straight sticks of different lengths and try to arrange them into a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/introduction-to-types-of-triangles\/\">triangle<\/a> with one of the sides longer than the other two combined. There\u2019s just no way to make it connect as a triangle!<\/p>\n<h2><span id=\"Angle_Sum_Property\" class=\"m-toc-anchor\"><\/span>Angle Sum Property<\/h2>\n<p>\nFor our second property, let\u2019s move from a rule about the <em>sides<\/em> of a triangle to one about the <em>angles<\/em> inside the triangle. You probably remember that the angles inside any triangle always add up to 180\u00b0. <\/p>\n<p>Since that\u2019s true, we can\u2019t have a triangle with two angles that are 90\u00b0 (a right angle) or more than 90\u00b0 (an obtuse angle). The reason why is simple \u2013 there wouldn\u2019t be any degrees left to make the third angle:<\/p>\n<div class=\"examplesentence\">\\(90^{\\circ}+90^{\\circ}+\\text{ third angle}=180^{\\circ}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe third angle here would have to be 0\u00b0, and an angle with that measure isn\u2019t any angle at all. And it\u2019s even worse if we use obtuse angles: <\/p>\n<div class=\"examplesentence\">\\(100^{\\circ}+95^{\\circ}+\\text{ third angle}=180^{\\circ}\\)<\/div>\n<p>\n&nbsp;<br \/>\nHere, our third angle would need to be \u201315\u00b0! That\u2019s just not going to work to make a triangle! <\/p>\n<h2><span id=\"Isosceles_Triangle_Theorem\" class=\"m-toc-anchor\"><\/span>Isosceles Triangle Theorem<\/h2>\n<p>\nFor the third property, we\u2019re going to examine the relationship between the sides of a triangle and their lengths. But first, we need to define the term <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/congruent-shapes\/\">congruent<\/a>. <strong>Congruent<\/strong> sides of a triangle are sides that are the same length. The length of a side congruent to a side that measures 5 centimeters would be 5 centimeters. The same is true for angles.<\/p>\n<p>In any triangle, if we have two sides that are congruent, then the two angles that are opposite those sides will also be congruent. This is always true no matter how long the two sides are or how tiny or big the angles are. We can see that in this triangle, which is an isosceles triangle. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65090\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/isosceles-triangle.png\" alt=\"isosceles triangle\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/isosceles-triangle.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/isosceles-triangle-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/isosceles-triangle-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/isosceles-triangle-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/isosceles-triangle-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<h2><span id=\"Midsegment_Theorem\" class=\"m-toc-anchor\"><\/span>Midsegment Theorem<\/h2>\n<p>\nFor our final property, let\u2019s look at this triangle:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65087\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-green-line-segment.png\" alt=\"triangle with green line segment\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-green-line-segment.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-green-line-segment-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-green-line-segment-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-green-line-segment-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-green-line-segment-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<p>Here, we have a line segment in green that connects the midpoint of one side to the midpoint of another side. Whenever you do this in a triangle, the line segment you created is always half the length of the side you didn\u2019t bisect. Not only that, it\u2019s parallel to that side too!<\/p>\n<hr>\n<p>\nAs you can see, triangles are amazing shapes with all sorts of cool properties.<\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<div style=\"text-align: center;\"><a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/area-and-perimeter-of-a-triangle\/\">Area and Perimeter of a Triangle<\/a> | <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/introduction-to-types-of-triangles\/\">Types of Triangles<\/a><\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Triangle_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Triangle Practice Questions<\/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 \/>\nThe theorem stating that no side of a triangle can be longer than the other two sides added together is known as the:<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">Pythagorean theorem<\/div><div class=\"PQ\"  id=\"PQ-1-2\">Equilateral triangle theorem<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">Triangle inequality theorem<\/div><div class=\"PQ\"  id=\"PQ-1-4\">Congruent triangle theorem<\/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>A triangle cannot have one side that is longer than the sum of the other two sides. For example, a shape with side lengths 16, 22, and 40 would not connect as a triangle. The two shorter side lengths are not long enough to reach and connect to form a triangle.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Triangle-Rules-Example-1.svg\" alt=\"A triangle with sides labeled 16, 22, and 40.\" width=\"481.1\" height=\"122.4\" class=\"aligncenter size-full wp-image-287243\"  role=\"img\" \/><\/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 \/>\nThe interior angles of a triangle will always have a sum of _________. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">180\u00b0<\/div><div class=\"PQ\"  id=\"PQ-2-2\">150\u00b0<\/div><div class=\"PQ\"  id=\"PQ-2-3\">90\u00b0<\/div><div class=\"PQ\"  id=\"PQ-2-4\">360\u00b0<\/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>The interior angles of a triangle will always add to 180\u00b0. This means that a triangle cannot have more than one 90\u00b0 angle, and no more than one obtuse angle.<\/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 \/>\nThe following isosceles triangle shows two congruent side lengths, therefore angle _____ and angle _____ will be congruent.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Triangle-Rules-Example-2.svg\" alt=\"A triangle labeled ABC with sides AC and AB each 6.5 cm, and base CB 4 cm.\" width=\"284\" height=\"303\" class=\"aligncenter size-full wp-image-287246\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">Angle C and Angle A<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">Angle C and Angle B<\/div><div class=\"PQ\"  id=\"PQ-3-3\">Angle A and Angle B<\/div><div class=\"PQ\"  id=\"PQ-3-4\">No angles will be congruent<\/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>If two sides lengths of a triangle are congruent, then the corresponding angles will also be congruent. <\/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 \/>\nBeth is creating a stone walking path through a triangular green space in her city. She sketches a diagram of the park and labels it triangle ABC. Beth wants the path to start at the midpoint of side AB and end at the midpoint of side BC as drawn below. If this is how the path is designed, what will be true regarding the length of DE compared to AC?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Triangle-Rules-Example-3.svg\" alt=\"A triangle ABC with points D and E on sides AB and BC, respectively, and line segment DE parallel to AC.\" width=\"353\" height=\"280\" class=\"aligncenter size-full wp-image-287249\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">DE will be twice as long as AC.<\/div><div class=\"PQ\"  id=\"PQ-4-2\">DE will be congruent to AC.<\/div><div class=\"PQ\"  id=\"PQ-4-3\">DE will be exactly one-fourth the length of AC.<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">DE will be exactly half the length of AC.<\/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>If you connect the midpoint of one side of the triangle to the midpoint of another side, the distance from point to point will be exactly half of the side that you did not bisect. In this example, the distance of DE will be exactly half of AC.<\/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 \/>\nPoint A is the midpoint of XY, and point B is the midpoint of YZ. If the distance of AB is half the distance of XZ, determine the value of x.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Triangle-Rules-Example-4.svg\" alt=\"Triangle XYZ with a line segment AB parallel to side YZ; AB is labeled with length 3x-1. Points A and B are on sides XY and XZ, respectively.\" width=\"371\" height=\"213\" class=\"aligncenter size-full wp-image-287240\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(x=5\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">\\(x=6\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(x=7\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(x=8\\)<\/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>When you connect the midpoint of one side of a triangle to the midpoint of another side of the triangle, the line segment will be exactly half of the side length that was not bisected.<\/p>\n<p>In this example, AB is exactly half the distance of XZ. This means that \\(3x-1\\) is half of 34. Half of 34 is 17, so we can set \\(3x-1\\) equal to 17 and solve for \\(x\\).<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(3x-1=17\\)<br \/>\n\\(3x=18\\)<\/p>\n<p>When both sides of the equation are divided by 3, the result is \\(x=6\\).<\/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>\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":185933,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-58895","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":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58895","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=58895"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58895\/revisions"}],"predecessor-version":[{"id":246493,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58895\/revisions\/246493"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/185933"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=58895"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}