8.3 Methods of Proving Triangles Similar

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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.