Section 4.5 – Using Congruent Triangles
Q
Question: How could I prove that PQS  RQS in the diagram on the right?
P
R
S
CPCTC means “_____________________________________________________________________________________
_________________________________________________________________________________________________.”
Examples:
1. Given: A is the midpoint of MT , A is the midpoint of SR .
Prove:
Fill in the reasons in the following proof.
Statements
Reasons
1. A is the midpoint of MT ;
A is the midpoint of SR .
2. MA  TA ; SA  RA
1.
3. MAS  TAR
3.
4. MAS  TAR
4.
5. M  T
5.
6.
6.
2.
2. If you are given that
, use a paragraph proof to show
.
M
3. Given: MP bisects LMN ; LM  NM
Prove: LP  NP
L
N
P
Fill in the missing statements and reasons.
Statements
Reasons
1. MP bisects LMN
1.
2.
2. Definition of Angle Bisector
3. MP  MP
3.
4. LM  NM
4.
5.
5. SAS
6.
6.