Overlapping Triangles Lesson 3.5

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

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

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

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

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

Statement Reason Given 1. 1 is comp to 2. 2. 3 is comp to 4. 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