Which of the following choices must be true in order for abc = edc by the aas congruency theorem?

ABC = EDC by the AAS congruency theorem

answer
<A = <E

hope it helps

To use the AAS Theorem, you need two angles in a row followed by a side in each triangle.
Let's see what we have.

1) We have sides BC and CD congruent. That is a pair of sides.

2) Following those two sides, we have vertical angles which are congruent. They are angles BCA and DCE.

So far, we have a pair of sides and a pair of angles. Now we need another pair of angles.

3) You need angles A and E to be congruent. This would give you angle-angle-side.

Choice B.