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There are three ways to determine similarity:

  1. The AAAA Postulate: Two triangles are similar iff 2 of their corresponding angles are congruent. We don't need the third one since the sum of the measures of the angles of a triangle equals 180∘180^\circ.

  2. The SSSSSS Postulate: Two triangles are similar iff all of their corresponding sides are in proportion.

  3. The SASSAS Postulate: Two triangles are similar iff 2 of their corresponding sides are in proportion and the angle in between is congruent.

Worth the struggle

Twenty minutes on one hard problem can teach more than ten easy exercises. These problems are worth staying with. 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.

Type a concept, like “slope” or “photosynthesis”.

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