Question 817965: Hi! How are you? I have a question pertaining to writing a proof.
This is what the figure looks like: http://imgur.com/1y9Jh6m
Given: Triangle ABF is congruent to triangle DFB, F is the midpoint of segment AE, and B is the midpoint of segment AC.
Prove: Triangle FDE is congruent to triangle BCD is congruent to triangle ABF (it's proving the three triangles are congruent to each other).
I tried it on my own, and I came up with the fact that, due to the definition of a midpoint, segment AF is congruent to segment FE and segment AB is congruent to segment BC.
The problem is, I'm not sure how to find out the other side or angle measures -- I'm stuck, and I don't know what to do next.
Thank you in advance for any and all help!
Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website! Notice that the big outer triangle is similar to the triangle on the top,
since the side lengths are proportional ( Can be developed from the
midpoint information ). This means that angle AEC = angle AFB, and
angle ACE = angle ABF. Notice also that angle FDB = angle FAB since they
are opposite the same side of congruent triangles.
Let me know if this lets you finish. I was playing with vertical angles and
the like to try to get further.
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