What are What are Congruent Congruent

figures?figures?

Lesson 3.1Lesson 3.1

Understand the concept of congruent Understand the concept of congruent figures and accurately identify the figures and accurately identify the

corresponding parts of figures.corresponding parts of figures.

Congruent figuresCongruent figures: Same size, same shape: Same size, same shape AllAll sides, angles, and points the same sides, angles, and points the same Match up the sameMatch up the same

Ex.1: B YEx.1: B Y

A C X ZA C X ZIf ABC = XYZIf ABC = XYZ

thenthen A A X, X, B B Y, Y, C C Z Z

andand AB AB XY, BC XY, BC YZ, CA YZ, CA ZX ZX

* Notice letters match up in order* Notice letters match up in order

Definition: Definition: all pairs of all pairs of corresponding parts are corresponding parts are ..

“ “implies” “If..., then...”implies” “If..., then...”

the statement is reversiblethe statement is reversible

In later chapters In later chapters polygons all polygons all pairs of corresponding parts are pairs of corresponding parts are ..

K K

I EI E

TT

Ex. 2: ITK ETKIK EKIT ETKT KT (all use the reflexive property)

Name Name Name Name

Name Name Sides Sides

KET is a reflection of KITKET is a reflection of KIT IKT IKT EKT EKT KET KET KIT KIT

Postulate: any segment or Postulate: any segment or angle is congruent to itself angle is congruent to itself (reflexive property)(reflexive property)

Try to justify each conclusion with one of the Try to justify each conclusion with one of the properties presented in Chapter 2 and in this section.properties presented in Chapter 2 and in this section.

A. Multiplication PropertyB. Subtraction PropertyC. SubstitutionD. Reflexive Property