Question

P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. If AD = 10 cm, then CD =

(a) 5 cm

(b) 6 cm

(c) 8 cm

(d) 10 cm

Answer 1

Parallelogram ABCD is given such that

We haveand

We need to find the measure of side CD.

Since and AP as transversal

But it is given that

Therefore, we get:

Also, sides opposite to equal angles are equal.

Then,

…… (I)

Also,

Substituting in (I), We get:

It is given that , this means opposite side ,as ABCD is a parallelogram. Therefore,

Or,

Hence the correct choice is (a).