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7-5 Theorems for Similar Triangles Theorem 7-1 – SAS Similarity Theorem – If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar D A Given: <A <D AB AC DE DF B Prove: ▲ABC ~ ▲DEF C E F *Remember – the angle must be in-between the proportional sides Theorem 7-2 – SSS Similarity Theorem – If all three sides of two triangles are in proportion, then the triangles are similar. D AB BC AC Given: DE EF DF A Prove: ▲ABC ~ ▲DEF B C E F **When testing if two triangles have proportional sides, set up the proportion with the smallest side of one to the smallest side of the other, the largest of one to the largest of the other, and so on. Examples: 1. The measures of the sides of ▲ABC are 4, 5, and 7, and the measures of the sides of ▲XYZ are 16, 20, and 28. Are the two triangles similar? If so, why? 2. In triangle ▲ABC, AB = 2, AC = 5, and BC = 6. In ▲XYZ, XY = 2.5, YZ = 2, and XZ = 3. Is ▲ABC ~ ▲XYZ? If so, why? Pg 264 (Classroom exercises) 1-9