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

Correct option is C

Given:

ABCD is a parallelogram

P is the midpoint of BC

∠BAP = ∠DAP

AD = 10 cm

Solution:

In a parallelogram, opposite sides are equal.

AD = BC

AB = CD

In a parallelogram, opposite sides are parallel.

AD || BC

AB || DC

Since AD || BC, ∠DAP = ∠APB (Alternate interior angles)

Given: ∠BAP = ∠DAP

Therefore, ∠BAP = ∠APB

In triangle ABP, since ∠BAP = ∠APB, AB = BP (Sides opposite to equal angles are equal)

AD = 10 cm (Given)

BC = AD = 10 cm

P is the midpoint of BC, so BP = PC =$$\frac{BC }{ 2} = \frac{10 cm }{ 2}$$​= 5 cm

AB = BP = 5 cm

CD = AB = 5 cm

Therefore, CD = 5 cm.