SOLUTION: Hi! I am really stumped on this geometry question. I will try my best to explain the problem without a diagram. I am asked to write a two-column proof. Given is isosceles trapezoi

Question 248692: Hi! I am really stumped on this geometry question. I will try my best to explain the problem without a diagram.
I am asked to write a two-column proof. Given is isosceles trapezoid ABCD, with the top and bottom bases (AD and BC) being parallel. There is a line extending from angle D to point E, point E appearing to be the midpoint of BC. This line makes the left leg of triangle EDC, and it is given that DE is congruent to DC. I have to prove that ABED is a parallelogram.
I have tried several methods, and just when I think I'm solving the problem, I realize something is missing. I would really appreciate your help. Thank you.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
it is an isosceles trapezoid which means that AB and DC are the same size and have the same angle at abc and dcb
if de and dc are congruent they are have the same angle too.
we can show that angle ade must be the same as dec because of the line de intersecting parallel lines ad and bc
so ab and de are parallel

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