{"id":7326,"date":"2016-07-14T09:57:11","date_gmt":"2016-07-14T16:57:11","guid":{"rendered":"https:\/\/magoosh.com\/sat\/?p=7326"},"modified":"2016-11-11T07:59:01","modified_gmt":"2016-11-11T15:59:01","slug":"sat-math-triangles","status":"publish","type":"post","link":"https:\/\/magoosh.com\/sat\/sat-math-triangles\/","title":{"rendered":"SAT Math: Similar and Congruent Triangles"},"content":{"rendered":"<p>Because triangles have so many interesting properties that build upon each other, you can count on seeing them on the SAT. Although the problems that you will encounter won&#8217;t necessarily be difficult, <strong>the key lies in being able to figure out which property or concept to use in order to get to the answer.<\/strong><\/p>\n<p>Here you will be tested on figuring out missing side lengths, and you&#8217;ll have to brush up on some triangle knowledge before we begin:<\/p>\n<ul>\n<li>The sum of interior angles in a triangle add up to 180 degrees.<\/li>\n<li>The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle equals the square of the longest side (the hypotenuse).<\/li>\n<\/ul>\n<h2>SAT Math: Similar Triangles<\/h2>\n<p><a href=\"https:\/\/magoosh.com\/sat\/act\/act-math-tips-similar-triangles\/\">Similar triangles<\/a> have the same angle measure for all angles, but they don&#8217;t necessarily have equal side lengths. All triangles with the same angle measures are similar.<\/p>\n<p>The side lengths of similar triangles are proportional to each other, so we can set up a ratio in order to figure out missing side lengths:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-7327\" src=\"https:\/\/magoosh.com\/sat\/files\/2016\/06\/Triangles.gif\" alt=\"SAT Math Triangles -magoosh\" width=\"318\" height=\"213\" \/><\/p>\n<p style=\"text-align: center\">Photo by\u00a0<a href=\"http:\/\/jwilson.coe.uga.edu\/emt668\/emat6680.folders\/brooks\/6690stuff\/righttriangle\/trig.html\" target=\"_blank\" rel=\"nofollow noopener noreferrer\">jwilson<\/a><\/p>\n<p>A\/E = B\/F = C\/G<\/p>\n<h2>SAT Math: Congruent Triangles<\/h2>\n<p>Congruent triangles are the same size, so they have the same angle measurements and equal side lengths. In other words, they are basically the same triangle.<\/p>\n<h2>SAT Math: Sample Triangle Problem<\/h2>\n<p>Let&#8217;s take a look at a sample problem:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-7327\" src=\"https:\/\/magoosh.com\/sat\/files\/2016\/06\/Triangles.gif\" alt=\"SAT Math Triangles -magoosh\" width=\"318\" height=\"213\" \/><\/p>\n<p>Triangle ADG (above) has an area of 6 square units. If AD = AF = 3, then what is the length of EF?<\/p>\n<p>A) 12\/5<br \/>\nB) 2<br \/>\nC) 8\/3<br \/>\nD) 1\/2<\/p>\n<p>1. The first thing we want to do here is label our given measurements. Whenever we have a problem that asks us to use or draw a reference picture, we always want to write and draw everything out. Let&#8217;s mark down the length of sides AD and AF.<\/p>\n<p>2. Since the area of the entire triangle is given, we can go ahead and solve for the missing side length DG using area = (\u00bd)base*height. In this case, we should get<br \/>\n6 = .5*3*height<br \/>\n4 = height<\/p>\n<p>Side length DG is equal to 4.<\/p>\n<p>3. Now we can either use the Pythagorean Theorem to solve for side length AG or see that we have a 3-4-5 right triangle. Either way, we should get 5 for the length of side AG.<\/p>\n<p>4. From here, recognize that since both triangle AEF and ADG share an angle (angle A) and are both right triangles, they must be similar. Therefore, we can set up a ratio between the two triangles in order to solve for length EF.<\/p>\n<p>We will use the two known hypotenuse lengths and the length of DG.<\/p>\n<p>3\/5 = x\/4<\/p>\n<p>x = 12\/5<\/p>\n<p>Our answer here is A!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Because triangles have so many interesting properties that build upon each other, you can count on seeing them on the SAT. Although the problems that you will encounter won&#8217;t necessarily be difficult, the key lies in being able to figure out which property or concept to use in order to get to the answer. Here [&hellip;]<\/p>\n","protected":false},"author":158,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[],"ppma_author":[24918],"class_list":["post-7326","post","type-post","status-publish","format-standard","hentry","category-all"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>SAT Math: Similar and Congruent Triangles<\/title>\n<meta name=\"description\" content=\"Because triangles have so many interesting properties that build upon each other, you can count on seeing them on the SAT. 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