Prove Corollary- Geometry?

Corollary - A proposition that follows from (and is often appended to) one already proved.

I like to think of them as "mini-theorems" that are a direct result of the bigger theorem.

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

let's say you have quadrilateral ABCD such that it is a parallelogram.

Introduce segment AC with the Line Postulate

AC=AC because of the reflexive property

segment AB is parallel to segment CD by definition of parallelogram

angle BAC is congruent to angle DCA by PAI Theorem ( If two parallel lines are cut by a transversal, then alternate interior angles are congruent)

segment AD is parallel to segment BC by definition of parallelogram

angle DAC is congruent to angle BCA by PAI Theorem

by ASA, triangle ADC is congruent to triangle CBA

AB=DC, AD=BC by CPCTC --> Opposite sides of a parallelogram are congruent