4-8 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

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Warm Up Lesson Presentation Lesson Quiz.

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

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

Objective Use CPCTC to prove parts of triangles are congruent.

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.

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

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

Example 2 Continued WY ZW

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

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.