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

2. Warm-up
Identify the postulate or theorem that proves the triangles congruent. HL
ASA
SAS or SSS

3. 4. Given: PN bisects MO, PN  MO
Warm-up
4. Given: PN bisects MO, PN  MO
Prove: ∆MNP  ∆ONP
1. Given
2. Def. of bisect
3. Reflex. Prop. of 
4. Given
5. Def. of 
6. Rt.   Thm.
7. SAS
1. PN bisects MO
2. MN  ON
3. PN  PN
4. PN  MO
5. PNM and PNO are rt. s
6. PNM  PNO
7. ∆MNP  ∆ONP
Reasons
Statements

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

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

10. Check It Out! Example 2 Continued
PR bisects QPS
and QRS
QRP  SRP
QPR  SPR
Given
Def. of  bisector
RP  PR
Reflex. Prop. of 
∆PQR  ∆PSR
PQ  PS
ASA
CPCTC

11. 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

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

13. 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.

14. Given: J is the midpoint of KM and NL.
Check It Out! Example 3
Prove: KL || MN
Given: J is the midpoint of KM and NL.

15. Check It Out! Example 3 Continued
Statements
Reasons
1. Given
1. J is the midpoint of KM and NL.
2. KJ  MJ, NJ  LJ
2. Def. of mdpt.
3. KJL  MJN
3. Vert. s Thm.
4. ∆KJL  ∆MJN
4. SAS
5. LKJ  NMJ
5. CPCTC
6. KL || MN
6. Conv. Of Alt. Int. s Thm.

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

17. Lesson Quiz: Part I Continued
4. Reflex. Prop. of 
4. P  P
5. SAS
5. ∆QPB  ∆RPA
6. CPCTC
6. AR = BQ
3. Given
3. PA = PB
2. Def. of Isosc. ∆
2. PQ = PR
1. Isosc. ∆PQR, base QR
Statements
1. Given
Reasons

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

19. Lesson Quiz: Part II Continued
5. CPCTC
4. ASA
4. ∆AXD  ∆CXB
6. Def. of mdpt.
6. X is mdpt. of BD.
3. Vert. s Thm.
3. AXD  CXB
2. Def. of midpt.
2. AX  CX
1. Given
1. X is mdpt. of AC. 1  2
Reasons
Statements
5. DX  BX