Proving in Geometry

Question

Given: AB ∥ DE

Prove: ΔABC ≅ ΔEDC

The figure is like an hourglass and the midpoint C.

What is the reason/theorem in these given statements:

AB ∥ DE -

∠A ≅ ∠E ; ∠B ≅ ∠D -

∠1 ≅ ∠2 -

ΔABC ≅ ΔEDC -

Answer 1

It would be super useful to see the picture that goes with this problem because with the information given, it is not possible to prove the triangle are congruent as there are no sides listed. Proving triangles are congruent requires one of the following:

SSS (side-side-side)

SAS (side-angle-side)

AAS (angle-angle-side)

ASA (angle-side-angle)

HL (for right triangles only and stands for hypotenuse-leg)

Notice that every one of these has a side included.

I will tell you this much. The reasons for AB ∥ DE is "Given" and the reasons for ∠A ≅ ∠E ; ∠B ≅ ∠D is "Alternate Interior Angles Theorem". Most likely the reason for ∠1 ≅ ∠2 is the "Vertical Angles Theorem".

But beyond that, without seeing the picture, I can't help since at least one set of corresponding sides must be congruent to prove triangle congruence (the proof needs another line in it that states two sides are congruent).