Question

Can someone please help me with this geometry proof? It needs to get done ASAP and I'm really struggling.

Answer 1

One way to prove that the triangles are congruent is to show that the three pairs of sides have the same length.

For side $BD$, this is easy, since it is shared by the two triangles, so it is obviously equal.

On the other hand, we know that the given figure is a parallelogram, the opposite sides are equal in length. Particularly, it means that:

$AB = CD \quad\textrm{and}\quad BC = AD.$

Thus, we have shown that each pair of sides have the same length, which means that:

$\triangle ABD \equiv \triangle CDB.$