Proving that the midponts of an isosceles trapezoid are collinear

Question

I am trying to prove that the midpoints of the parallel sides of an isosceles trapezoid are perpendicular in order to prove that the lines have identical perpendicular bisectors, but I cannot find a way to prove such a thing.

Answer 1

This question needs clarification and reformulation. For instance, what does it mean that "the midpoints of the parallel sides of an isosceles trapezoid are congruent" Two points are always congruent.