Write an indirect proof to show that opposite sides of a parallelogram are congruent. be sure to create and name the appropriate geometric figures.

We consider the two triangles in the figure above. in the figure,

1. the line ac is a transversal of parallel lines ab and cd,therefore angle cab and acd are alternate angles.

2.   line ac is a transversal of parallel lines bc and da, therefore angle acb and angle cad are alternate angles

3. ac = ca

triangles abc and cda are congruent. thus, ab = cd and bc = da.