Proof to show that a quadrilateral is a paralellogram.

Question

I am new to this site and I don't know how to code yet, so bear with me.

I am trying to show that the quadrilateral ABCD in the picture below is a parallelogram.

I know that since triangle EBC is isosceles, angle 1 and angle 2 are of equal size. Since angle 2 and angle 4 are of equal measure, then angle 1 and angle 4 are of equal measure. Then since angle 2 and angle 3 are of equal measure, so are angle 3 and angle 4. I don't know what to do next! Please help me, thank you!!

Answer 1

if angle 2 = angle 3, then BC is parallel to AD. and if angle 1 = angle 4 then DC is parallel to AB. And if you have a quadrilateral with both pairs of opposite edges parallel to one another you have a ?