Example 1: Using the AA ∼ Postulate, show why these triangles are similar ∠ BEA ≅∠ DEC because vertical angles are congruent ∠ B ≅∠ D because their measures are both 600 ΔBAE ∼ ΔDCE by AA ∼ Postulate.
Theorems Angle-Angle Similarity (AA ∼ ) Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Side-Angle-Side Similarity (SAS ∼ ) 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. Side-Side-Side Similarity (SSS ∼ ) Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar. Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Corollary to the Side-Splitter Theorem: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. Triangle-Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Wrap-up Today you learned to prove triangles similar and to use the Side-Splitter and Triangle-Angle-Bisector Theorems. Tomorrow you’ll learn about Similarity in Right Triangles Homework (H) p. 436 # 4-19, 21, 24-28 p. 448 # 1-3, 9-15 (odd), 25, 27, 32, 33 Homework (R) p. 436 # 4-19, 24-28 p. 448 # 1-3, 9-15 (odd), 32, 33