Question

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

विकल्प

• 5 cm

• 6 cm

• 8 cm

•  10 cm

Answer 1

Parallelogram ABCD is given such that ∠BAP = ∠DAP

We haveAD = 10cm and `BC = 1/2 BC`

We need to find the measure of side CD.

Since BC || AD and AP as transversal

∠I = ∠DAP

But it is given that

∠BAP = ∠DAP

Therefore, we get:

∠I = ∠BAP

Also, sides opposite to equal angles are equal.

Then,

AB = BP …… (I)

Also, `BP = 1/2 BC`

Substituting`BP = 1/2 BC`in (I), We get:

`AB = 1/2 BC`

It is given that AD = 10cm, this means opposite side BC = 10cm,asABCD is a parallelogram. Therefore,

 `AB = 1/2 (10cm)`

  AB = 5cm

Or, CD = 5cm

Hence the correct choice is (a).