Question

I put D but I am not sure if that is the valid answer. Any help?

Answer 1

Answer: B) ASA

Explanation:

AB || DC means we know that angle ABD = angle CDB. They are alternate interior angles. This is shown as the red angle markers in the diagram below.

Similarly, AD || BC leads to angle DBC = angle BDA. They are also alternate interior angles and they are marked in green in the diagram below.

So far we have two pairs of congruent angles.

The pair of congruent sides is BD = BD by the reflexive property. Any segment is congruent to itself.

So we can use ASA to prove the triangles congruent. Note the segment BD is between the angles mentioned.