Question

In the diagram given, AB is parallel to DC. If M is the midpoint of AC, must it also be the midpoint of BD? Why?

Answer 1

See explanation

Explanation:

Since m∠B = m∠D because alternate interiors angles are congruent when the lines are parallel

and m∠BMA = m∠CMC because vertical angles are congruent

and it AM = MC because it is given that M is the midpoint of AC, then

ΔBMA is congruent to ΔDMC.

Therefore, BM = DM because corresponding parts of congruent triangles are congruent.

Now, M is the midpoint of BD because BM = DM