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Objectives Prove that two triangles are similar using AA, SAS, and SSS

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**Proving Two Triangles Similar with Shortcuts**

Instead of using the definition of similarity to prove that two triangles are congruent (all corresponding angles are congruent and all corresponding sides are proportional), you can use three shortcuts: Angle-Angle (AA) Side-Angle-Side (SAS) Side-Side-Side (SSS)

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**Angle-Angle (AA) Similarity Postulate**

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

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AA Example Explain why the triangles are similar and write a similarity statement. ∠R ≅ ∠V (Given) ∠RSW ≅ ∠VSB (vertical angles are congruent) ΔRSW ≅ ΔVSB (AA)

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**Side-Angle-Side (SAS) Similarity Theorem**

If an angle of one triangle is congruent to an angle of a second triangle and the sides including the two angles are proportional, then the triangles are similar. G A 2 4 B C 3 J 6 H ΔABC ~ ΔGJH

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SAS Example Explain why the two triangles are similar and write a similarity statement. ∠Q ≅ ∠X since they are right angles The two sides that include the right angles are proportional By SAS, ΔPRQ ~ΔZYX

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**Side-Side-Side (SSS) Similarity Theorem**

If the corresponding sides of two triangles are proportional, then the triangles are similar. G A 4 5 8 10 B C 6 J 12 H ΔABC ~ ΔGJH

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SSS Example Explain why the two triangles are similar and write the similarity statement. Since all sides of the two triangles are proportional, by SSS, ΔABC ~ ΔEFG

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