Warm-up Identify the postulate or theorem that proves the triangles congruent.

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.

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

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

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

Example 3 Continued Statements Reasons 1. 1. 2. NOM  PMO 2. 3. 3. Reflex. Prop. of  4. ∆MNO  ∆OPM 4. 5. 5. 6. MN || OP 6. Conv. Of Alt. Int. s Thm.

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.

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. 3. 3. Vert. s Thm. 4. 4. SAS 5. LKJ  NMJ 5. 6. 6.

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

Lesson Quiz: Part I Continued 4. 4. P  P 5. 5. ∆QPB  ∆RPA 6. 6. AR = BQ 3. 3. PA = PB 2. Def. of Isosc. ∆ 2. PQ = PR 1. Statements Reasons

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.

Lesson Quiz: Part II Continued 5. 4. 4. ∆AXD  ∆CXB 6. 3. 3. AXD  CXB 2. 2. AX  CX 1. Reasons Statements