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If two pairs of corresponding angles in two triangles are equal, then the two triangles are similar. From two angles, we can find the third angle by taking minus the sum of the other two angles.
For example, in and , if and , then .
This is probably the most common way to prove that two triangles are similar in Olympiad problems.
These problems have no steps to copy. You have to understand the idea well enough to bend it to a new purpose. These are real problems from the AMC 8, AMC 10, AMC 12 and AIME, the national math competitions for middle and high school students, each with a worked solution on LIVE by Po-Shen Loh.
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A nice example of "oppositely similar" triangles appears in the antiparallel line configuration described by Zi Song Yeoh.
(They're called oppositely similar since the triangles have opposite orientation---the lines are called antiparallel, after all. If we had parallel lines instead, the triangles would be directly similar instead.
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Hello, I am attaching the same worksheet I have attached for SAS, please try problems 4, 5, 8, and 9. Have fun!
