{"id":10968,"date":"2012-04-20T09:00:12","date_gmt":"2012-04-20T16:00:12","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=10968"},"modified":"2012-04-13T16:59:06","modified_gmt":"2012-04-13T23:59:06","slug":"isosceles-triangles-on-the-gmat","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/isosceles-triangles-on-the-gmat\/","title":{"rendered":"Isosceles Triangles on the GMAT"},"content":{"rendered":"

\"\"The GMAT quantitative section asks, among other things, about geometry. One of the GMAT's favorite figures is the\u00a0isosceles<\/strong>\u00a0triangle.\u00a0 An isosceles triangle is one that has two congruent sides.\u00a0 Knowing simply that about a triangle has profound implications for answer GMAT Problem Solving & Data Sufficiency questions.<\/p>\n

 <\/p>\n

Euclid's Remarkable Theorem<\/h2>\n

Euclid first proved this theorem over 2200 years ago. \u00a0The theorem says:<\/p>\n

If the two sides are equal, then the opposite angles are equal<\/strong><\/p>\n

and<\/p>\n

if the two angles are equal, then the opposite sides are equal.<\/strong><\/p>\n

 <\/p>\n

It can be used for deductions in both directions (logically, this is called a \"biconditional\" statement\"). \u00a0Another way to say this: a statement about equal angles is sufficient to conclude equal sides; conversely, a statement about equal sides is sufficient to conclude equal angles.\u00a0 Remember that on GMAT Data Sufficiency!<\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

Isosceles Triangles and the 180\u00ba Triangle Theorem<\/h2>\n

Another favorite GMAT geometry fact is that the sum of all three angles in a triangle \u2212 any triangle \u2212 is 180\u00ba.\u00a0 This is particularly fruitful if combined with the Isosceles Triangle Theorem.<\/p>\n

Suppose you are told that Triangle ABC is isosceles, and one of the bottom equal angles (called a \"base angle\") is 50\u00ba.\u00a0 Then immediately you know that the measure of the other base angle is also 50\u00ba, and that means the top angle (the \"vertex angle\") must be 80\u00ba.\u00a0 Knowing the measure of one base angle is sufficient to find the measures of all three angles of an isosceles triangle.<\/p>\n

Suppose you are told that Triangle ABC is isosceles, and the vertex angle is 50\u00ba.\u00a0 Well, you don't know the measures of the base angle, but you know they're equal. Let x be the degrees of the base angle; then [pmath]x + x + 50\u00ba = 180\u00ba right 2x = 130\u00ba right x = 65\u00ba[\/pmath].\u00a0 So, each base angle is 65\u00ba.\u00a0 Knowing the measure of the vertex angle is sufficient to find the measures of all three angles of an isosceles triangle.<\/p>\n

BUT, if you are told that Triangle ABC is isosceles, and one of angles is 50\u00ba, but you\u00a0don't know\u00a0whether that 50\u00ba is a base angle or a vertex angle, then you cannot conclude anything about the other angles in the isosceles triangle without more information.\u00a0 That's a subtle but important distinction to remember on GMAT Data Sufficiency.<\/p>\n

 <\/p>\n

Free Practice Questions on Triangles<\/h2>\n

https:\/\/gmat.magoosh.com\/questions\/1019<\/a><\/p>\n

https:\/\/gmat.magoosh.com\/questions\/1024<\/a><\/p>\n

This post was written by Mike McGarry, GMAT Expert at\u00a0Magoosh<\/a>, and originally posted\u00a0here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

The GMAT quantitative section asks, among other things, about geometry. One of the GMAT’s favorite figures is the\u00a0isosceles\u00a0triangle.\u00a0 An isosceles triangle is one that has two congruent sides.\u00a0 Knowing simply…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,717,736],"tags":[],"class_list":["post-10968","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-problem-solving-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10968","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/133"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=10968"}],"version-history":[{"count":2,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10968\/revisions"}],"predecessor-version":[{"id":10972,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10968\/revisions\/10972"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=10968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=10968"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=10968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}