In parallelogram abcd, one way to prove that diagonals and bisect each other is to prove triangle axb congruent to triangle cxd. which triangle congruency theorem proves that the triangles are congruent? asa sss sas aas

The answer is: AAS

Proving that two triangles are congruent by AAS can be verified when two angles and a non-included side in the first triangle are equal to their corresponding two angles and non-included side in the second triangle.

For the given parallelogram (check attachment):
angle AXB = angle CXD (opposite angle)
angle ABX = angle CDX (alternate angles)
AB = CD (opposite sides in parallelogram are equal)
Therefore,
Triangle AXB is congruent to triangle CXD.