1. 3.5 Proofs Involving Overlapping Triangles

2. Overlapping Triangles
Some triangle relations are difficult to see because the triangles overlap.
To make things easier separate and redraw the triangles. A C B E F D A C B E F E F D

3. Proofs with Overlapping Triangles
Given: 1 =  2, AB  BF, CD  DE, BE = FD
Prove: ΔAFB = ΔCED
Since the two triangles you want to prove overlap, redraw and separate them. A B C D E F G 1 2

4. Proofs with Overlapping Triangles
Now that they are separated, mark the diagrams by what’s given to help you visualize what you have and what you need A C 1 2 B E F E F D A C 1 2 B E F E F D

5. Proofs with Overlapping Triangles
Now that they are separated you can see what you have and what you need a little clearer.
What You Have: Rt ’s, 1 = 2 and part of a line segment
What You Need: The completion of the line segment to prove the triangles are congruent using ASA.
Write the proof! A C 1 2 B E F E F D

6. You Try! Given: AD = AE A B C Part a: Prove: ΔADC ΔAEB Part b: D E
Continue the proof
and prove DC = EB A D E B C

7. You Try Another!
What additional given information would allow us to prove ?

8. You Try Another!
In an umbrella frame, the stretchers are congruent and they open to angles of equal measure.
Prove the angles created by the shaft and the ribs are congruent.

9. You Try Another!