8.6 Congruent Polygons

1. 8.6 Congruent Polygons

2. A correspondence is a way of matching up two sets of objects. Congruentfigures have the same shape and size. If two polygons are congruent, all of their corresponding sides and angles are congruent. To write a congruence statement, the vertices in the second polygon have to be written in the SAME order of correspondence with the first polygon.

3. 55 55 Example 1 A. Write a congruence statement for each pair of polygons. A corresponds to Q. A@Q B corresponds to R. B@R C corresponds to P.C@P The congruence statement is ABC@QRP.

4. Example 2 A. Write a congruence statement for each pair of congruent polygons. A B | A corresponds to S. A@S 60° 60° || |||| B corresponds to T. B@T 120° 120° ||| D C C corresponds to Q. C@Q Q R D corresponds to R. D@R ||| 120° 120° || |||| The congruence statement is trapezoid ABCD@ trapezoid STQR. 60° 60° | T S

5. WX @ KL a + 8 = 24 –8 –8 a = 16 Example 3 In the figure, quadrilateral VWXY@ quadrilateral JKLM. A. Find a. Subtract 8 from both sides.

6. ML @ YX 6b = 30 6b = 30 6 6 Example 4 In the figure, quadrilateral VWXY@ quadrilateral JKLM. B. Find b. Divide both sides by 6. b = 5

7. J @V 5c = 85 5c = 85 5 5 Example 5 In the figure, quadrilateral VWXY@ quadrilateral JKLM. C. Find c. Divide both sides by 5. c = 17