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

Question

P is the mid-point of side BC of a parallelogram ABCD such that &#x2220; BAP = &#x2220; DAP. If AD=10 cm, then CD=

Philoid · Accepted Answer

Given that,

ABCD is a parallelogram

P is the mid-point of BC

∠DAP =∠PAB =x

AD=10 cm

To find: The length of CD

∠ABP = 180 - 2x (Co interior angle of parallelogram)

∠APB = 180^o - (180^o - 2x + x) = x

Therefore,

In triangle ABP,

∠APB =∠PAB = x

Therefore,

AB = PB (In a triangle sides opposite to equal angles are equal in length)

CD = AB = PB = = = = 5 cm