Question

Inthe adjoining figure , M is the mid point of side BC of a parallelogram ABCD such that angle BAM = angle DAM. Prove that AD = 2CD​

Answer 1

Step-by-step explanation:

It is given that ABCD is a parallelogram

So we know that

AD || BC

From the figure we know that ∠ DAM and ∠ AMB are alternate angles

So we get ∠ DAM = ∠ AMB

We know that ∠ BAM = ∠ DAM It can be written as ∠ BAM = ∠ AMB

From the figure we know that the sides opposite to equal angles are equal

So we get BM = AB

We know that the opposite sides of a parallelogram are equal AB = CD

So we can write it as

BM = AB = CD ……. (1)

We know that M is the midpoint of the line BC

So we get BM = ½ BC

We know that BC = AD

We get BM = ½ AD Based on equation (1)

CD = ½ AD

By cross multiplication AD = 2CD.

Hence proved....