Congruent Polygons October 2, 2015

Congruence Congruent () – have the same size and shape. Congruent Polygon – corresponding sides and angles are all congruent Corresponding – sides and angles that have the same position in different figures

∆ABC  ∆YXZ ∆BAC  ∆XYZ  A  Y B  X  C  Z  Y X Z A B C Ex 1 Corresponding Angles Corresponding Sides  A  Y B  X  C  Z 

 A  M B  N  C  O   D  P Ex 2 Identify corresponding sides and corresponding angles of the congruent polygons. Corresponding Angles Corresponding Sides  A  M B  N  C  O   D  P

 A  P B  N  C  M  D  P  Ex 3 B N A C M O D P Identify corresponding sides and corresponding angles of the congruent polygons. Corresponding Angles Corresponding Sides  A  P B  N  C  M  D  P 

 M  U I  Z  H  E  K  S  F  L  Ex 4 Identify corresponding sides and corresponding angles of the congruent polygons. MIHKL  UZESF Corresponding Angles Corresponding Sides  M  U I  Z  H  E  K  S  F  L 

∆ABD  ∆CDB  A  C  BDA  DBC ABD  CDB  Identify corresponding sides and corresponding angles of the congruent polygons. A B C D ∆ABD  ∆CDB Corresponding Angles Corresponding Sides  A  C  BDA  DBC ABD  CDB 

Are the triangles congruent? If so, write a congruence statement. 1. Are corresponding angles congruent? Yes 2. Are corresponding sides congruent? Yes Yes, they are congruent. ∆PMN  ∆SRT

Are the quadrilaterals congruent? If so, write a congruence statement. 1. Are corresponding angles congruent? Yes 2. Are corresponding sides congruent? Yes Yes, they are congruent. CFED  LMJK

Are the triangles congruent? If so, write a congruence statement. 1. Are corresponding angles congruent? Yes 2. Are corresponding sides congruent? No No, they are not congruent.

Length of a Line Segment “Segment AB” “Length of Segment AB”

Segments are congruent when they have the same length. D 3 in G H 3 in Segment Lengths are equal (same size) CD = GH Segments are congruent (same size and shape) When writing out lengths, use the = sign. CD = 3 in

Are the following figures congruent? 1. Are they the same shape? Yes (segments) 2. Are they the same size? No (10 in  15 in) Not Congruent

Are the following figures congruent? 3 m 3 m 1. Are they the same shape? Yes (segments) 2. Are they the same size? Yes (both 3m) Congruent

A B C the angle’s name the angle’s measure

Angles are congruent when they have equal measures (same # of degrees). X A 50° 50° Z C Y B Angle Measures equal (same size/degrees) Angles are Congruent (size and shape same) When writing angle measures, use the = sign.

Are the following figures congruent? Ex 1 Are the following figures congruent? 130 130 1. Are they the same shape? Yes (angles) 2. Are they the same size? Yes (both 130) Congruent

Ex. 2 Are the following figures congruent? 45 50 1. Are they the same shape? Yes (angles) 2. Are they the same size? No (both 50  45) Not Congruent