Objectives:- Define congruent polygons- Solve problems by using congruent

polygons

4.1 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?

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:

ABCDEF AFEDCBBCDEFA BAFEDCCDEFAB CBAFEDDEFABC DCBAFEEFABCD EDCBAFFABCDE FEDCBA

Example: What are all of the possible names for the hexagon below?

A

B

C

D

E

F

Example:

The polygons at the right are congruent. Write a congruence statement about them.

A

B

D

CG

H

F

E

ABCD EFGH There is more than one way to write a congruence statement. Complete the congruence statements below.

BCDA _____

CBAD _____

CDAB _____

DABC _____

ADCB _____

BADC _____

Corresponding Sides & AnglesIf 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

DC

G

H

F

E

http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory

Example: Prove that ∆REX

R

E

XF

Note: Six congruences are required for triangles to be congruent—three pairs of angles and three pairs of sides.

Homework:

Pages 213–215; Numbers 7-28