Chapter 4.6 Notes: Use Congruent Triangles

Goal: You will use congruent triangles to prove that corresponding parts are congruent.

Properties of Congruent Triangles

A D

B C E F

What pairs of angles and sides are congruent? ____________________________________________________________________________________

ABC DEF

Using CPCTC:

• Once you know that triangles are congruent, you can make conclusions about corresponding sides and angles because Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Ex.1: Suppose you know that by SAS. Which additional pairs of sides and angles are congruent by CPCTC? A B

1 2

D 4 C

ABD CDB

Ex.2: Explain how you can prove that

Ex.3: Complete the proof.

Given:

Prove: A D

1 2

C

B E

.A C

,AC EC BC DC A E

Ex.4: Complete the proof.

Given: bisects

Prove:

F

K G

H

GK &FGH FKH FK HK

Ex.5: Complete the proof.

Given:

Prove:

1 2, RTQ RTS QT ST

Ex.6: Complete the proof.

Given:

Prove:

1 2, 3 4 BCE DCE

Ex.7: Complete the proof.

Given:

Prove:

O

N P

M Q

1 2, 3 4 MNR QPR