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4-6

4-6. Triangle Congruence: CPCTC. Holt Geometry. Warm Up. Lesson Presentation. Lesson Quiz. Do Now 1. If ∆ ABC  ∆ DEF , then  A  ? and BC  ? . 2. If 1  2, why is a||b ?. Objective. U se CPCTC to prove parts of triangles are congruent. Vocabulary. CPCTC.

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4-6

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  1. 4-6 Triangle Congruence: CPCTC Holt Geometry Warm Up Lesson Presentation Lesson Quiz

  2. Do Now • 1. If ∆ABC  ∆DEF, then A  ? and BC  ? . • 2.If 1  2, why is a||b?

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

  4. Vocabulary CPCTC

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

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

  8. Example 2 A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK?

  9. Given:YW bisects XZ, XY YZ. Z Example 3: Proving Corresponding Parts Congruent Prove:XYW  ZYW Reasons Statements 1. Given 2. Given 3. Def. segment bisector 4. Reflexive POC 5. SSS 6. CPCTC

  10. Given:PR bisects QPS and QRS. Prove:PQ  PS Example 4 Reasons Statements 1. Given QRS 2. Def.  bisector 3. Def.  bisector 4. Reflexive POC 5. ASA 6. CPCTC

  11. Helpful Hint 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.

  12. Given:NO || MP, N P Prove:MN || OP Example 5: Using CPCTC in a Proof 1 3 4 2 Reasons Statements 1. Given 2. Given 3. Alt. int.  th. 4. Reflexive POC 5. AAS 6. CPCTC 7. Converse of alt. int.  th.

  13. Given:J is the midpoint of KM and NL. Prove:KL || MN Example 6 3 1 Reasons Statements 2 4 1. Given 2. Def. midpoint 3. Def. midpoint 4. Vertical  th. 5. SAS 6. CPCTC 7. Converse of alt. int.  th.

  14. You Try It! Given: X is the midpoint of AC . 1 2Prove: X is the midpoint of BD. 4 3 Reasons Statements 1. Given 2. Given 3. Def. midpoint 4. Vertical  th. 5. ASA 6. CPCTC 7. Def. midpoint

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