1. Objective
Use CPCTC to prove parts of triangles are congruent.

2. Vocabulary
CPCTC

3. 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.

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

5. Example 1: Engineering Application
A and B are on the edges of a ravine. What is AB?

6. Check It Out! Example 1
A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK?

7. Then look for triangles that contain these angles.
Work backward when planning a proof. To show that ED || GF, look for a pair of angles that are congruent.
Then look for triangles that contain these angles.
Helpful Hint

8. Example 2: Using CPCTC in a Proof
Prove: MN || OP
Given: NO || MP, N  P

9. Example 2 Continued
Statements
Reasons
1. N  P; NO || MP
1. Given
2. NOM  PMO
2. Alt. Int. s Thm.
3. MO  MO
3. Reflex. Prop. of 
4. ∆MNO  ∆OPM
4. AAS
5. NMO  POM
5. CPCTC
6. MN || OP
6. Conv. Of Alt. Int. s Thm.