Which theorem proves that the triangles are congruent? a) asa b) sas c) ssa d) sss

Hello!

Looking at the image above, we are given that side BE is congruent to side ED while side AE is congruent to side EC. This can be written as follows:

BE = ED
AE = EC

In this case, ∠1 and ∠2 can be classified as vertical angles. Vertical angles are the two angles on opposite sides of two intersecting lines. These angles are always congruent to one another. Consequently, ∠1 and ∠2 must also be congruent to one another. This can be written as follows:

∠1 = ∠2

We have now proven the congruency of two sides and one angle. Because the angle lies between the two sides, this implies the use of SAS (side-angle-side).

Therfore, the correct answer is B.

I hope this helps!