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Objectives: Define congruent polygons Solve problems by using congruent polygons

4.1 Congruent Polygons. 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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Objectives: Define congruent polygons Solve problems by using congruent polygons

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  1. 4.1 Congruent Polygons 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?

  2. Polygon Congruence Postulate: • 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

  3. Example: What are all of the possible names for the hexagon below? B ABCDEF AFEDCB BCDEFA BAFEDC CDEFAB CBAFED DEFABC DCBAFE EFABCD EDCBAF FABCDE FEDCBA C A F D E

  4. Example: The polygons at the right are congruent. Write a congruence statement about them. ABCD EFGH There is more than one way to write a congruence statement. Complete the congruence statements below. D BCDA _____ H G C ADCB _____ CBAD _____ F DABC _____ B BADC _____ A E CDAB _____

  5. 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. H B 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. G E A C F D

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

  7. Homework: • Pages 213–215; Numbers 7-28

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