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Transcript
CHAPTER 7 Similarity Theorems 1. Angle-Angle Similarity (AA~) Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. 2. 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. 3. Side-Side-Side Similarity (SSS~) Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar. 4. Right Triangle Theorem: The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. 5. Heartbeat Corollary 6. Nike Swoosh Corollary: 7. 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. 8. Corollary to the Side-Splitter Theorem : If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. 9. 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.