Question

3. In the adjoining figure, M is the midpoint of A
ZBAM = ZDAM. Prove that AD = 2CD.
side BC of a parallelogram ABCD such that
D
B
M​

Answer 1

Answer:

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

so

∠BAM=∠AMB

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

so we get

BM=AB

we know the opposite sides of a parallelogram are equal

AB=CD

so we can write it as

MB=AB=CD....(1)

we know that M is midpoint of the line BC

so we get

BM=1/2BC

we know that BC=AD

we get

MB=1/2AD

based on equation (1)

CD=1/2AD

by cross multiplication

AD=2CD

therefore it is proved that AD=2CD

Hope this is helpful for you.