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Know Your Similar Triangles For The SAT Math (Part 1)

Know Your Similar Triangles For The SAT Math (Part 1)

Certain diagrams appear frequently on SAT. Whenever you see a triangle inside a triangle or two triangles with the same angle measurements, most likely you will be looking at similar triangles. The following diagrams are the most commonly appearing similar triangles.

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What are similar triangles?

Two triangles are similar if they have the same shape but not necessarily the same size. The most common way to identify whether two triangles are similar on SAT is testing for Angle-Angle (AA) similarity. We have an AA similarity when two triangles have two corresponding angles equal to each other.

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In the diagram above, we have two vertical sides parallel to each other. The angles marked in red are congruent since they are vertical angles, and the angles marked in blue are congruent since they are the alternate interior angles. Therefore these two triangles are similar.

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In the second diagram above, there is a smaller triangle inside a larger triangle, and we have two parallel bases. The angle marked in blue is shared by the two triangles, and the two angles marked in red are congruent since they are corresponding angles. Therefore, these two triangles are similar.

The most difficult part about similar triangles is identifying them. Many students often see a diagram with triangles and try to utilize everything they know about a triangle to solve the problem, yet fail to recognize the similarity between the two triangles. Hopefully, now that we have learned about common diagrams of similar triangles, you will be able to spot the similarity at a glance. In the next post, we will learn about how we can use this information to solve SAT problems.

Do you have questions about similar triangles or want to learn more about topics in geometry that appear in SAT? LionRock Education offers classes that cover a variety of topics in SAT Math. Join our SAT class to learn more and improve your score.

What’s Next?

Want more tips on how to study the SAT?  Check out our online and in-person programs here.

We offer both online and in-person programs. Along with expert-led classes, you'll get personalized SAT report with results organized by topics so you study most effectively. We'll also provide you a complete SAT strategy guide to follow so you'll learn all the necessary topics.


About the Author

Soo believes mathematics could be a tool that can be used to understand the world in a deeper, more meaningful way. Unfortunately many students often get intimidated by math, and Soo works with students from various backgrounds to overcome that fear and find joy of problem solving. Soo supports girls and women in STEM field as well and believes anyone can pursue STEM major. She earned her B.S. in Mathematics from UCLA and tutors students in SAT mathematics and high school math courses.