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8.3 METHODS OF PROVING TRIANGLES SIMILAR AAA In order to prove triangles are similar we need to start with a Postulate. • AAA: If three angles correspond to the other triangle’s three angles, then the triangles are similar. AA The following are theorems that will be used in proofs. • AA: If two corresponding angles of one triangle correspond to the other two angles of the other triangle, then the triangles are similar. Ex: G: <A congruent <D <B congruent <E C: ABC = DEF SSS~ SSS~ :If the three sides of the triangles are proportional then the triangles are similar. Ex: G: Prove: ABC ~ DEF SAS~ SAS~ : If two of the triangles sides are proportional and the included angles are congruent, then the two triangles are similar. Ex: G: <B = <E P: ABC ~ DEF CPCTC If you are given the two triangles are similar, then • 1. Corresponding sides of the triangles are proportional (The ratios of the measures of corresponding sides are equal.) • 2. Corresponding angles of the triangles are congruent.