1. 4-8 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry

2. Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ? .
2. What is the distance between (3, 4) and (–1, 5)?
3. If 1  2, why is a||b?
4. List methods used to prove two triangles congruent. D EF
17
Converse of Alternate Interior Angles Theorem
SSS, SAS, ASA, AAS, HL

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

4. Vocabulary
CPCTC

5. 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.

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

7. Example 2: Proving Corresponding Parts Congruent
Given: YW bisects XZ, XY  YZ.
Prove: XYW  ZYW Z

8. Example 2 Continued WY ZW

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

10. Example 3 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.