1. Lesson 2.1 Lesson 2.1 Congruent polygons

2. Lesson 6.5 Congruent Polygons 2 March 21, 2016 Lesson 2.1 Objectives Identify Congruent Figures. Name Corresponding Parts. Prove Triangles Congruent. Essential Question: How can you tell if polygons are congruent?

3. Lesson 6.5 Congruent Polygons 3 March 21, 2016 Congruent Figures Two figures are congruent if they have exactly the same shape and same size. These figures are congruent:

4. Lesson 6.5 Congruent Polygons 4 March 21, 2016 So are these:

5. Lesson 6.5 Congruent Polygons 5 March 21, 2016 These are not congruent:

6. Lesson 6.5 Congruent Polygons 6 March 21, 2016 If two figures are congruent, then there is a correspondence between them. A B C Corresponding Angles  A   R  B   S  C   T Corresponding Sides AB  RS AC  RT BC  ST  ABC   RST Congruence Statement R S T

7. Lesson 6.5 Congruent Polygons 7 March 21, 2016  ABC   RST You could also write:  BAC   SRT  CAB   TRS  ACB   RTS  BCA   STR  CBA   TSR A B C R S T

8. Lesson 6.5 Congruent Polygons 8 March 21, 2016 But you cannot write:  ABC   RTS  B is NOT congruent to  T. When writing a congruence statement, corresponding parts must be matched correctly. A B C R S T

9. Lesson 6.5 Congruent Polygons 9 March 21, 2016 Example Write a congruence statement for these congruent figures. C A B D M N R S ABCD  NSRM CDAB  RMNS BADC  SNMR ADCB  NMRS

10. Lesson 6.5 Congruent Polygons 10 March 21, 2016 Example In this diagram,  RST   XYZ. R S T X Y Z 40° 12 85°  S  ______ YZ = ______ m  S = ______  X  ______ RS = ______ m  X = ______ YY 12 85° RR XY 40°

11. Lesson 6.5 Congruent Polygons 11 March 21, 2016 Your Turn ABCD  KLHJ. Solve for x and y. AB CD L K J H 91° 86°113° (5y – 2)° 4x – 3 cm 9 cm 6 cm 4x – 3 = 9 4x = 12 x = 3 5y – 2 = 113 5y = 115 y = 23

12. Lesson 6.5 Congruent Polygons 12 March 21, 2016 Example A B C 22° 87° D E F (4x + 15)°  ABC   DEF. Find x. 71 71 = 4x + 15 56 = 4x x = 14