1. Overlapping Triangles
Lesson 3.5

2. 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

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
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 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