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