Lionel is given the diagram below and asked to prove

ASA Triangle Congruence Theorem

A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. In every parallelogram the diagonals bisect each other, so the statement we need to prove is true.

Since opposite sides of every parallelogram are congruent and alternating interior angles are congruent and vertical angles are congruent, then we get the First Figure below. As you can see, we have two triangles, one on the top and one on the bottom. So they are congruent by A.S.A postulate that tells us that if triangles have matching angles and a matching side length between the angles, they're definitely congruent. And this is shown in the second figure below.

AAS congruence theorem

Step-by-step explanation: