{"id":12895,"date":"2021-06-13T00:28:00","date_gmt":"2021-06-12T18:58:00","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=12895"},"modified":"2022-11-23T16:43:58","modified_gmt":"2022-11-23T11:13:58","slug":"gmat-geometry-formulas-concepts-on-triangles-part-1","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/gmat-geometry-formulas-concepts-on-triangles-part-1\/","title":{"rendered":"GMAT Geometry Formulas and Concepts on Triangles (Part 1)"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">6<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"150\" height=\"150\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/Most-Common-Mistakes-in-GMAT-Geometry-Questions-2-150x150.png\" alt=\"GMAT Geometry Formulas | GMAT Quant Concepts \" class=\"wp-image-12868\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/Most-Common-Mistakes-in-GMAT-Geometry-Questions-2-150x150.png 150w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/Most-Common-Mistakes-in-GMAT-Geometry-Questions-2.png 282w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/figure>\n\n\n\n<p>Do you feel overwhelmed while learning a plethora of GMAT Geometry formulas and concepts? Do you feel Geometry is your weak topic? You are not alone. Many test takers avoid solving GMAT Geometry questions, as most of them don\u2019t feel comfortable with this topic.<\/p>\n\n\n\n<p>In this article, you will read-<\/p>\n\n\n\n<ul><li><a href=\"#GMAT_Geometry\">Why is GMAT Geometry your weak area?<\/a><\/li><li><a href=\"#help_improve_GMAT_Geometry\">How will we help you improve Geometry?<\/a><\/li><li><a href=\"#basic_properties_triangles_gmat_geometry\">Basic properties of triangles for GMAT Geometry<\/a><\/li><li><a href=\"#examples\">Illustrative examples showing usage of GMAT Geometry Formulas<\/a><\/li><li><a href=\"#takeaways\">Takeaways<\/a><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"1283\" height=\"468\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant.png\" alt=\"GMAT Geometry formulas | Geometry formulae | GMAT Quant prep for GMAT Geometry\" class=\"wp-image-12897\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant.png 1283w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-300x109.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-768x280.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-1024x374.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-1080x394.png 1080w\" sizes=\"(max-width: 1283px) 100vw, 1283px\" \/><\/figure>\n\n\n\n<h2 id=\"h-\">&nbsp;<\/h2>\n\n\n\n<ol><li>There are <u>too many GMAT Geometry formulas to remember<\/u>. Even though GMAT tests us on a very limited number of properties, but since these limited properties are not collated in a single place, it is difficult for a test taker to confidently say he knows all the concepts.<\/li><li>And say, even if someone <u>manages to find and learn all the concepts<\/u>, most of them are not sure how to apply these concepts to <u>deduce information from the given question and figure<\/u> in the questions tested on the GMAT.<\/li><\/ol>\n\n\n\n<blockquote><p><strong><u>NOTE:<\/u><\/strong> This is the second article in our GMAT Geometry Pitfalls series. Do read the first article click on the link below.<\/p><p><em><a href=\"https:\/\/e-gmat.com\/blogs\/most-common-mistakes-in-gmat-geometry-questions-gmat-quant-prep\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Most common mistakes in GMAT Geometry Questions<\/a><\/em><\/p><p>The next 2 articles in this series are:<\/p><ul>\n<li class=\"entry-title\"><a href=\"https:\/\/e-gmat.com\/blogs\/geometry-practice-questions-properties-of-triangles\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">GMAT Geometry Practice Questions \u2013 Properties of Triangles (Part 2)<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/e-gmat.com\/blogs\/geometry-practice-problems-gmat-special-properties-of-triangles\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Geometry Practice Problems and Special Properties of Triangles (Part 3)<\/a><\/li>\n<\/ul><\/blockquote>\n\n\n\n<h2 id=\"h-how-will-we-help-you-with-gmat-geometry-prep\"><span id=\"help_improve_GMAT_Geometry\">How will we help you with GMAT Geometry Prep?<\/span><\/h2>\n\n\n\n<p>In this article, we will address both the above issues by:<\/p>\n\n\n\n<ul><li>Consolidating the <u>MOST important GMAT Geometry concepts needed in Triangles<\/u>.<\/li><li><u>Focusing on some GMAT-like and official questions<\/u> and illustrating the application of the above concepts in these questions.<\/li><\/ul>\n\n\n\n<h2 id=\"h-basic-properties-of-triangles\"><span id=\"basic_properties_triangles_gmat_geometry\">Basic properties of triangles<\/span><\/h2>\n\n\n\n<p>This section covers the following aspects:<\/p>\n\n\n\n<ul><li>Finding if a set of given numbers could be the lengths of a triangle or not<\/li><li>The range of values the side of a triangle can take given the values of the other two sides, and<\/li><li>The properties of the <u>angles of the triangle<\/u><\/li><\/ul>\n\n\n\n<h2 id=\"h-concept-1-gmat-geometry-formulas\">Concept 1: GMAT Geometry formulas<\/h2>\n\n\n\n<h5 id=\"h-geometry-gmat-concept-1-sum-of-lengths-of-any-two-sides-of-a-triangle-length-of-the-third-side\"><strong>Geometry GMAT Concept 1 &#8211; Sum of lengths of any two sides of a triangle &gt; Length of the third side<\/strong><\/h5>\n\n\n\n<p>Suppose you are given three lengths a, b, and c, and asked to find out if we can form a triangle using these three lengths.<\/p>\n\n\n\n<p><em>How are you going to approach this problem?<\/em><\/p>\n\n\n\n<p><strong><u>Theory:<\/u><\/strong><\/p>\n\n\n\n<p>To determine if the three lengths will form a triangle or not, we need to know <u>the most basic property of a triangle:<\/u><\/p>\n\n\n\n<p>Sum of lengths of any two sides of a triangle &gt; Length of the third side<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"300\" height=\"234\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-1-300x234.png\" alt=\"GMAT geometry formulas formulae GMAT quant prep\" class=\"wp-image-12898\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-1-300x234.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-1.png 382w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p>This means that:<\/p>\n\n\n\n<ul><li><strong>a + b &gt; c<\/strong><\/li><li><strong>b + c &gt; a<\/strong><\/li><li><strong>c + a &gt; b<\/strong><strong>&nbsp;<\/strong><\/li><\/ul>\n\n\n\n<p>Please note that <u>all the three inequalities should satisfy<\/u>&nbsp;for the triangle to exist.<\/p>\n\n\n\n<p>Let us understand this with the help of a very basic GMAT-like question:<\/p>\n\n\n\n<h2 id=\"h-illustrative-example-1\"><span id=\"examples\">Illustrative Example 1<\/span><\/h2>\n\n\n\n<p>Q. The three lengths 5, 3, and x are used to form a triangle. Which of the following can be the value of x?<\/p>\n\n\n\n<ol><li>6<\/li><li>9<\/li><li>10<\/li><li>12<\/li><li>14<\/li><\/ol>\n\n\n\n<p>Since 5, 3 and x form a triangle, they must satisfy the property \u2013<\/p>\n\n\n\n<p><strong>Sum of lengths of any two sides of a triangle &gt; Length of the third side<\/strong><\/p>\n\n\n\n<p>Therefore, we can write \u2013<\/p>\n\n\n\n<p><strong>I. 5 + 3 &gt; x&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; II.&nbsp; 3 + x &gt; 5&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;III. 5 + x &gt; 3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>&nbsp; =&gt; x &lt; 8&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=&gt; x &gt; 2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =&gt; x &gt; -2<\/strong><\/p>\n\n\n\n<p>we can conclude that the range of x is: 2 &lt; x &lt; 8<\/p>\n\n\n\n<p>Out of the given options, the only option that falls within this range is 6. Hence, <strong>option A is our answer.<\/strong><\/p>\n\n\n\n<p>Therefore, now we know:<\/p>\n\n\n\n<ul><li>How to find if the <u>given lengths form a triangle or not<\/u><\/li><li>How to use the above property to <u>find the range of values for an unknown side in a triangle<\/u><\/li><\/ul>\n\n\n\n<h2 id=\"h-concept-2-gmat-geometry-formulas\">Concept 2: GMAT Geometry Formulas<\/h2>\n\n\n\n<p>Suppose after finding out that the given lengths form a triangle, you want to find out how the length of the sides can help in <strong>finding a relation between the angles of the triangle.<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p>To understand this, we need to know two more important properties:<\/p>\n\n\n\n<h5 id=\"h-gmat-geometry-concept-2-the-sum-of-the-interior-angles-of-a-triangle-is-constant-and-is-equal-to-180\"><strong>GMAT Geometry Concept 2 &#8211;&nbsp;<\/strong><strong>The sum of the interior angles of a triangle is constant and is equal to 180\u00b0<\/strong><\/h5>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"300\" height=\"259\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-2-300x259.png\" alt=\"GMAT geometry formulas formulae GMAT quant prep\" class=\"wp-image-12899\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-2-300x259.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-2.png 343w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p>Please note that the above property holds true for all triangles irrespective of their size and shape.<\/p>\n\n\n\n<p><u>&nbsp;<\/u><em><u>(Notice I am using capital A, B and C to denote the angles of the<\/u><\/em><\/p>\n\n\n\n<p><u>&nbsp;<\/u><em><u>triangle and a, b, and c for the lengths of the sides of the triangle)<\/u><\/em><\/p>\n\n\n\n<h5 id=\"h-property-3-in-any-triangle-the-largest-side-is-always-opposite-the-largest-angle-and-the-smallest-side-is-always-opposite-the-smallest-angle\">Property 3 &#8211; In any triangle, the largest side is always opposite the largest angle and the smallest side is always opposite the smallest angle<\/h5>\n\n\n\n<p>Let me explain this a bit more in detail:<\/p>\n\n\n\n<p>If ABC is a triangle, in which we know that the lengths AB, BC, and CA follow the relation AB&gt;BC&gt;AC, then we can conclude that, since <u>AB is the greatest side the angle opposite to it<\/u> <u>i.e., angle ACB is the greatest angle<\/u>.<\/p>\n\n\n\n<p>And since BC &gt; AC, angles opposite to them also hold the same relation, that means angle BAC &gt; angle ABC<\/p>\n\n\n\n<p>Hence we can conclude that: \u2220 ACB &gt; \u2220 BAC &gt; \u2220 ABC<strong><em>&nbsp;<\/em><\/strong><\/p>\n\n\n\n<p>Keep in mind that the <strong>converse is <u>also<\/u> true<\/strong>, i.e., if <u>the relation between the angles is given, we<\/u> <u>can use that to find the relation between the sides.<\/u><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><em>The devil is in the details! Planning out the finer details of your study schedule takes you one step closer to your target GMAT score. Learn the other benefits of a <\/em><strong><a href=\"https:\/\/e-gmat.com\/blogs\/gmat-study-plan-benefits-study-plans-100-score-improvement\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">well defined study plan<\/a><\/strong><em> in this article.<\/em><\/p><cite>Save 60+ hours of GMAT preparation by crafting a well-defined study plan in just 3 steps:<\/cite><\/blockquote>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/5ftgtAl_3C0? rel=0\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer rel=0; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\"><\/iframe>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-c21dc048-4b52-4896-bdf4-fe6abbc67c21\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/create-study-plan\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 576, 512\"><path fill=\"currentColor\" d=\"M144.3 32.04C106.9 31.29 63.7 41.44 18.6 61.29c-11.42 5.026-18.6 16.67-18.6 29.15l0 357.6c0 11.55 11.99 19.55 22.45 14.65c126.3-59.14 219.8 11 223.8 14.01C249.1 478.9 252.5 480 256 480c12.4 0 16-11.38 16-15.98V80.04c0-5.203-2.531-10.08-6.781-13.08C263.3 65.58 216.7 33.35 144.3 32.04zM557.4 61.29c-45.11-19.79-88.48-29.61-125.7-29.26c-72.44 1.312-118.1 33.55-120.9 34.92C306.5 69.96 304 74.83 304 80.04v383.1C304 468.4 307.5 480 320 480c3.484 0 6.938-1.125 9.781-3.328c3.925-3.018 97.44-73.16 223.8-14c10.46 4.896 22.45-3.105 22.45-14.65l.0001-357.6C575.1 77.97 568.8 66.31 557.4 61.29z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Create your Personalized Study Plan<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<p>Let us understand the application of this property through an example:<\/p>\n\n\n\n<h2 id=\"h-illustrative-example-2\">Illustrative Example 2<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"300\" height=\"225\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-3-300x225.png\" alt=\"GMAT geometry formulas formulae GMAT quant prep\" class=\"wp-image-12900\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-3-300x225.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant-3.png 336w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p>In the triangle given below, all the points denoted are non-overlapping and the angles A, B, and C are distinct. Is AB &gt; AC &gt; BC?<\/p>\n\n\n\n<ol><li>\u2220 y<sub>1<\/sub> = \u2220 c<sub>1<\/sub><\/li><li>\u2220 BAC &lt; \u2220 ABC and neither angle is the greatest in the triangle ABC<\/li><\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p><strong><u>Approach<\/u><\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p>We need to find if the statement AB &gt; AC &gt; BC is true or not. For this, it is enough to get a relation among angles A, B and C since <u>the sides of a&nbsp;<\/u><u>triangle follow<\/u> <u>the same relation as the angles opposite to them.<\/u><\/p>\n\n\n\n<p><strong><u>Analyze Statement 1<\/u><\/strong><\/p>\n\n\n\n<p><strong>&nbsp;<\/strong>\u2220<strong>y<sub>1<\/sub> = <\/strong><strong>&nbsp;<\/strong>\u2220<strong>c<sub>1<\/sub><\/strong><\/p>\n\n\n\n<p>Therefore, in \u0394BYC<\/p>\n\n\n\n<p>BY = BC<\/p>\n\n\n\n<p>But AB = BY + YA<\/p>\n\n\n\n<p>AB &gt; BC<\/p>\n\n\n\n<p>However, <u>we cannot infer any relationship between BC and AC (or AB and AC)<\/u> from the given information<\/p>\n\n\n\n<p><strong><u>Analyze Statement 2<\/u><\/strong><\/p>\n\n\n\n<p><strong>Given <\/strong>\u2220 <strong>BAC &lt; <\/strong>\u2220 <strong>ABC and neither angle is the greatest.<\/strong><\/p>\n\n\n\n<p>Also, in the question statement, it is mentioned that angles BAC, ABC, and ACB are distinct, therefore, \u2220ACB has to be the greatest angle.<\/p>\n\n\n\n<p>Therefore, we can conclude, \u2220 <strong>BAC <\/strong>&lt; \u2220 <strong>ABC <\/strong>&lt; \u2220 <strong>ACB<\/strong><\/p>\n\n\n\n<p>Thus, we can conclude that length <strong>BC &lt; AC &lt; AB<\/strong><\/p>\n\n\n\n<p>Hence, statement 2 is sufficient to arrive at a unique answer.<strong><em>&nbsp;<\/em><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: B<\/strong><\/p>\n\n\n\n<h2 id=\"h-takeaways-article-1-gmat-geometry-triangle-concepts\"><span id=\"takeaways\">Takeaways &#8211; Article 1 &#8211; GMAT Geometry Triangle Concepts<\/span><\/h2>\n\n\n\n<p>This brings us to the end of the first article in this series. I hope you find it useful and informative. After reading this you should be able to easily:<\/p>\n\n\n\n<ol><li><strong><u>Apply GMAT Geometry Concept 1<\/u><\/strong>, to identify if a triangle can be formed from the given three lengths<\/li><li><u><\/u><strong><u>Apply GMAT Geometry Concept 1<\/u><\/strong>, to also find the range of the unknown side, if the other two lengths of the triangle are given<\/li><li><u><\/u><strong><u>Apply GMAT Geometry Concept 2<\/u><\/strong> in questions where the relation of angles and sides are required to solve the problem<\/li><\/ol>\n\n\n\n<p>Keeping these takeaways in mind, can you solve the 2 questions?<\/p>\n\n\n\n<ol><li><a href=\"http:\/\/gmatclub.com\/forum\/mastering-important-concepts-in-triangles-exercise-question-229646.html#p1768649\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\"><strong>Mastering Important Concepts Tested By GMAT in Triangles &#8211; Exercise Question #1<\/strong><\/a><\/li><li><a href=\"http:\/\/gmatclub.com\/forum\/mastering-important-concepts-in-triangles-exercise-question-229647.html#p1768655\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\"><strong>Mastering Important Concepts Tested By GMAT in Triangles &#8211; Exercise Question #2<\/strong><\/a><strong>&nbsp;<\/strong><\/li><\/ol>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>If you are planning to take the GMAT, we can help you with a personalized study plan and give you access to quality online content to prepare.<\/strong>&nbsp;<strong>Write to us at&nbsp;<a href=\"mailto:acethegmat@e-gmat.com\" target=\"_blank\" rel=\"noreferrer noopener\">acethegmat@e-gmat.com<\/a>. We are the&nbsp;<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">most reviewed GMAT prep company on gmatclub<\/a>&nbsp;with more than 2400 reviews&nbsp;<\/strong>and are the only prep company that has delivered&nbsp;<a href=\"https:\/\/e-gmat.com\/blogs\/e-gmat-review\/\" target=\"_blank\" rel=\"noreferrer noopener\" data-wpel-link=\"internal\">more than 700+ scores than any other GMAT club partner<strong>.<\/strong><\/a>&nbsp;<strong>Why don\u2019t you take a free trial and judge for yourself?<\/strong><\/p><\/blockquote>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-df0d119f-e04f-4a32-b980-efc953a3547c\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 512, 512\"><path fill=\"currentColor\" d=\"M256 0C114.6 0 0 114.6 0 256c0 141.4 114.6 256 256 256s256-114.6 256-256C512 114.6 397.4 0 256 0zM406.6 278.6l-103.1 103.1c-12.5 12.5-32.75 12.5-45.25 0s-12.5-32.75 0-45.25L306.8 288H128C110.3 288 96 273.7 96 256s14.31-32 32-32h178.8l-49.38-49.38c-12.5-12.5-12.5-32.75 0-45.25s32.75-12.5 45.25 0l103.1 103.1C414.6 241.3 416 251.1 416 256C416 260.9 414.6 270.7 406.6 278.6z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Start your free trial<\/span>\n    <\/div><\/a><\/div><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 448, 512\"><path fill=\"currentColor\" d=\"M246.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L178.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C47.63 444.9 55.81 448 64 448s16.38-3.125 22.62-9.375l160-160C259.1 266.1 259.1 245.9 246.6 233.4zM438.6 233.4l-160-160c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25L370.8 256l-137.4 137.4c-12.5 12.5-12.5 32.75 0 45.25C239.6 444.9 247.8 448 256 448s16.38-3.125 22.62-9.375l160-160C451.1 266.1 451.1 245.9 438.6 233.4z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Take a free mock<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<h5 id=\"h-in-the-next-articles-on-triangles-read-about\"><strong>In the next articles on Triangles, read about<\/strong><\/h5>\n\n\n\n<p><strong>1.&nbsp;&nbsp; <\/strong><u><a href=\"https:\/\/e-gmat.com\/blogs\/geometry-practice-questions-properties-of-triangles\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Tabular Representation<\/a>:<\/u>&nbsp;Different types of triangles with their MOST important properties.<\/p>\n\n\n\n<p><strong>2.&nbsp;&nbsp; <\/strong>&nbsp;<u><a href=\"https:\/\/e-gmat.com\/blogs\/geometry-practice-problems-gmat-special-properties-of-triangles\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Special Properties<\/a>:<\/u>&nbsp;A few special properties that can be tested by GMAT.<\/p>\n\n\n\n<p><a href=\"#_ftnref1\" name=\"_ftn1\">[1]<\/a> <em>Formulas<\/em>&nbsp;is the plural form of&nbsp;<em>formula<\/em>, the alternate plural of&nbsp;<em>formula<\/em>&nbsp;is&nbsp;<em>formulae.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do you feel overwhelmed while learning a plethora of GMAT Geometry formulas and concepts? Do you feel Geometry is your weak topic? You are not alone. Many test takers avoid solving GMAT Geometry questions, as most of them don\u2019t feel comfortable with this topic. In this article, you will read- Why is GMAT Geometry your [&hellip;]<\/p>\n","protected":false},"author":102406,"featured_media":12897,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[104,94,60],"tags":[],"featured_image_src":"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/06\/GMAT-geometry-formulas-concepts-GMAT-Quant.png","author_info":{"display_name":"Suheb Hussain","author_link":"https:\/\/e-gmat.com\/blogs\/author\/syede-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>GMAT Geometry Formulas and Concepts on Triangles (Part 1) | e-GMAT<\/title>\n<meta name=\"description\" content=\"Targeting a Q51 on GMAT? Need help with GMAT Quant Prep? 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