1. 5.7 Vocabulary
CPCTC
CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent.

2. SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. Use CPCTC AFTER congruent triangles.
Remember!

3. Example 1: Proving Corresponding Parts CongruentZ
Given: YW bisects XZ, XY  YZ.
Prove: XYW  ZYW

4. Check It Out! Example 2
Prove: PQ  PS
Given: PR bisects QPS and QRS.

5. Example 3: Using CPCTC in a Proof
Prove: MN || OP
Given: NO || MP, N  P

6. Example 4:
A and B are on the edges of a ravine. What is AB?

7. Example 5:
∆RST  ∆LMP. ST = 2x + 10, TR = 3x, MP = x + 30, LM = 2x + 5 find PL

8. Lesson Quiz: Part I
1. Given: Isosceles ∆PQR, base QR, PA  PB
Prove: AR  BQ

9. Lesson Quiz: Part II
2. Given: X is the midpoint of AC . 1  2
Prove: X is the midpoint of BD.

10. To prove Midpoint:
To prove Bisector:
To prove Isosceles: