Solving Similar Triangle Math Problems
Ah, similar triangles. An old ACT fav.
I like to think of them as mama and baby triangles; they look just alike, but one is bigger and one is smaller. It’s a little silly, but it’s a memory trick that’s helped a lot of my students.
Here’s the actual math definition: Similar triangles have congruent (the same) corresponding angle measures. Because all the angles in one triangle have the same measure as the corresponding angle in the other triangle, this means the sides of two similar triangles are in proportion to one another.
When you encounter a “similar triangle” problem on the ACT, you’ll know it because the question and/or diagram will clarify that the two triangles have the same angle measures.
Often the answer to the question will be the length of one of the missing sides, or you’ll be required to find the length of a missing side in order to unlock the next step in a more difficult problem.
The key is to find the ratio, or proportion between the side lengths. Typically this means setting up a proportion and cross-multiplying.
Example ACT Question:
Let’s say you are given these two triangles with the same angle measures and these side lengths given and asked to find the missing side:
Now you might be able to eyeball this one because it is relatively straightforward, but you can always set up a proportion:
And there you have it. You’ve found your missing side and can move onto the next ACT problem coming your way!
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About Kristin Fracchia
Dr. Kristin Fracchia makes sure Magoosh's sites are full of awesome, free resources that can be found by students prepping for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agony and bliss of trail running, backpacking, hot yoga, and esoteric knowledge.
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