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Objectives: - Define congruent polygons - Solve problems by using congruent polygons Warm-Up: Captain Frank and Professor Quantum played chess. They played seven games, each won the same number of games, and there weren’t any stalemates. How could this have happened?

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Two polygons are congruent if and only if there is a correspondence between their sides and angles such that: -each pair of corresponding angles is congruent -each pair of corresponding sides is congruent Polygon Congruence Postulate:

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ABCDEFAFEDCB BCDEFABAFEDC CDEFABCBAFED DEFABCDCBAFE EFABCDEDCBAF FABCDEFEDCBA Example: What are all of the possible names for the hexagon below? A B C D E F

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Example: The polygons at the right are congruent. Write a congruence statement about them. A B D C G H F E There is more than one way to write a congruence statement. Complete the congruence statements below.

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Corresponding Sides & Angles If two polygons have the same number of sides, it is possible to set up a correspondence between them by pairing their parts. In quadrilaterals ABCD and EFGH, for example, you can pair angles A&E, B&F, C&G, and D&H. Notice you must go in the same order around each of the polygons. A B D C G H F E

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http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theoryExample: R E X F Note: Six congruences are required for triangles to be congruent—three pairs of angles and three pairs of sides.

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Homework: Pages 213–215; Numbers 7-28

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7.4 A Postulate for Similar Triangles. We can prove that 2 triangles are similar by showing that all 3 corresponding angles are congruent, and all 3 sides.

7.4 A Postulate for Similar Triangles. We can prove that 2 triangles are similar by showing that all 3 corresponding angles are congruent, and all 3 sides.

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