Lesson 2 1 polygons Congruent Lesson 2 1

Lesson 2. 1 polygons Congruent

Lesson 2. 1 Objectives Identify Congruent Figures. n Name Corresponding Parts. n Prove Triangles Congruent. n Essential Question: How can you tell if polygons are congruent? 24 December 2021 Lesson 6. 5 Congruent Polygons 2

Congruent Figures n n Two figures are congruent if they have exactly the same shape and same size. These figures are congruent: 24 December 2021 Lesson 6. 5 Congruent Polygons 3

So are these: 24 December 2021 Lesson 6. 5 Congruent Polygons 4

These are not congruent: 24 December 2021 Lesson 6. 5 Congruent Polygons 5

If two figures are congruent, then there is a correspondence between them. C Corresponding Angles A R A B S B C T T Corresponding Sides AB RS S R ABC RST 24 December 2021 Congruence Statement Lesson 6. 5 Congruent Polygons BC ST AC RT 6

ABC RST C You could also write: BAC SRT A B T CAB TRS ACB RTS BCA STR R 24 December 2021 S CBA TSR Lesson 6. 5 Congruent Polygons 7

But you cannot write: ABC RTS C A B T R 24 December 2021 S B is NOT congruent to T. When writing a congruence statement, corresponding parts must be matched correctly. Lesson 6. 5 Congruent Polygons 8

Example Write a congruence statement for these congruent figures. A M B D C S R ABCD NSRM CDAB RMNS 24 December 2021 N BADC SNMR ADCB NMRS Lesson 6. 5 Congruent Polygons 9

Example In this diagram, RST XYZ. S Y 85° 12 40° R T X Z Y S ______ R X ______ 12 YZ = ______ XY RS = ______ 85° m S = ______ 40° m X = ______ 24 December 2021 Lesson 6. 5 Congruent Polygons 10

Your Turn ABCD KLHJ. Solve for x and y. A 9 cm B L 4 x – 3 cm 91° 86° D 113° 6 cm C (5 y – 2)° H 4 x – 3 = 9 5 y – 2 = 113 4 x = 12 5 y = 115 x=3 y = 23 24 December 2021 Lesson 6. 5 Congruent Polygons K J 11

Example ABC DEF. Find x. B E 87° A 71 22° (4 x + 15)° C D F 71 = 4 x + 15 56 = 4 x x = 14 24 December 2021 Lesson 6. 5 Congruent Polygons 12