1. 3.5 Overlapping Triangles Objective: After studying this lesson you will be able to use overlapping triangles in proofs.

2. Let’s look at this problem. At first we might try to prove. We could then say that angles D and C are congruent because of CPCTC Given: Prove: C A B D E But there is not enough information. We have to find two other angles to which D and C belong. Then we can prove the triangles congruent and their corresponding parts.

3. We can make overlapping triangles easier. C A B D E We can color the two triangles we are going to use. We can draw the triangles separately. BBA A D C

4. Given: Prove: Statement Reason 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. E C D A B

5. Given: Prove: Statement Reason 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8. M JH G F K

6. Summary: Don’t let overlapping triangles confuse you. Name ways that you can help to see where the overlapping triangles are. Homework: worksheet