THE CONGRUENCE STATEMENTΔABC ≅ΔVPI

What does it tell you?

1, 2, 3, 4, 5, SIX! If the triangles are congruent

by SSS, SAS,ASA, AAS, or HL, then three pairs of corresponding parts have been used.

Remember, there are six corresponding parts!

Consider the next proof.., List off the six corresponding parts. Check the ones that are used to

prove the triangles are congruent. See the left - overs. These may be used as congruent by

the Definition of Congruent Triangles.

This book uses the expression:

Corresponding Parts of Congruent Triangles are Congruent.

CPCTC

CPCTC stands for…

With SSS, SAS, ASA, and AAS, you know how to use 3 parts of triangles to show that the triangles are congruent.

Once you have triangles congruent you can make conclusions about their other parts because, by definition, corresponding parts of congruent triangles are congruent.

Corresponding Parts of Congruent Triangles are Congruent

Given: and Prove: XMQ RMTStatements Reasons 1. 1. Given2. 2. 3. 3. 4. 4. Def. of segment

bisector5. XMQ RMT5.

TRXQ ||

RXTQ ,

QTXR bisects

Changing the goal…

No longer is the goal to prove the triangles are congruent…

Now we want the PARTS!

Given: and Prove: Statements Reasons 1. 1. Given2. 2. 3. 3. 4. 4. Def. of segment

bisector5. 6. 5.XMQ RMT 5.

TRXQ ||

RXTQ ,

QTXR bisects __________

MRXM

TRXQ ||

QTXR bisects

You try this one…#29 pg. 199

Changing the goalProve: ________

TSQT

8.

1. Prove AB CB

2. Prove M R

3. Prove S O

4. Prove KP LM

5. Prove CT RP

6. Prove AMT RTM