{"id":7326,"date":"2016-07-14t09:57:11","date_gmt":"2016-07-14t16:57:11","guid":{"rendered":"\/\/www.catharsisit.com\/sat\/?p=7326"},"modified":"2016-11-11t07:59:01","modified_gmt":"2016-11-11t15:59:01","slug":"new-sat-math-triangles","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/sat\/new-sat-math-triangles\/","title":{"rendered":"new 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 new 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>new sat math: similar triangles<\/h2>\n<p><a href=\"\/\/www.catharsisit.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=\"\/\/www.catharsisit.com\/sat\/files\/2016\/06\/triangles.gif\" alt=\"new 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>new 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>new 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=\"\/\/www.catharsisit.com\/sat\/files\/2016\/06\/triangles.gif\" alt=\"new 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 new 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. [&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>new 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 new sat. click here for more.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/sat\/new-sat-math-triangles\/\" \/>\n<meta property=\"og:locale\" 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