ACT Math Tips: Similar Triangles | Video Post

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Kristin Fracchia

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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 Math section, 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:

ACT similar triangles example

Now you might be able to eyeball this one because it is relatively straightforward, but you can always set up a proportion:

ACT similar triangle proportion example

And there you have it. You’ve found your missing side and can move onto the next ACT problem coming your way!

Author

  • Kristin Fracchia

    Dr. Kristin Fracchia has over fifteen years of expertise in college and graduate school admissions and with a variety of standardized tests, including the ACT, SAT, GRE, GMAT, and LSAT, with several 99% scores. She had a PhD from the University of California, Irvine, an MA degree from The Catholic University, and BA degrees in Secondary Education and English Literature from the University of Maryland, College Park. She was the recipient of the 2013 Excellence in Teaching Award and the Chancellor’s Club Fellowship from the University of California, Irvine. She’s worked as a high school teacher and university professor, as an independent college and graduate school admissions counselor, and as an expert tutor for standardized tests, helping hundreds of students gain acceptance into premier national and international institutions. She now develops accessible and effective edtech products for Magoosh. Her free online content and YouTube videos providing test prep and college admissions advice have received over 6 million views in over 125 countries. Kristin is an advocate for improving access to education: you can check out her TEDx talk on the topic. Follow Kristin on LinkedIn!

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