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Exploring Overlapping Triangles: CPCTC Proof

Learn how to identify and match overlapping triangles, prove congruence using CPCTC, and apply properties to solve triangle relationships. Practice with visual aids and steps provided.

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Exploring Overlapping Triangles: CPCTC Proof

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  1. Overlapping Triangles Lesson 3.5

  2. What are overlapping triangles? A There are two triangles that overlap inside the larger triangle. Outline the overlapping triangles with different colored pencils or markers. D E C B

  3. Where are the overlapping triangles? Outline the overlapping triangles with different colored pencils or markers.

  4. Overlapping triangles can be matched by CPCTC. Given: AB  DC AC  DB Prove △ABC  △DCB D A E B C

  5. Statement Reason • AB  DC • AC  DB • BC  BC • ABC  DCB • Given • Given • Reflexive Property • SSS

  6. Given: <1 = <3 <1 comp <2 <3 comp <4 Conclusion: AB = CD D A E 3 1 2 4 B C

  7. Statement Reason • Given • Given • Given • Comps of s are . • Addition Prop. • Reflexive Prop. • ASA • CPCTC • 1. 1 is comp to 2. • 2. 3 is comp to 4. • 1  3 • 2  4 • ABC  DCB • BC  BC • ABC  DCB • AB  CD

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