### In a parallelogram ABCD, the bisector of ∠A also bisects the side BC. If AB = 6 cm, find the length of side AD.

**Answer:**

12 cm

**Step by Step Explanation:**

- According to the explanation given in the question, draw a parallelogram ABCD, Let us assume that bisector of ∠A meet at E and construct FE || CD and AB, as shown below:
**Given:**Bisector of ∠A bisect line BC into two equal parts.- Let us assume that AD = x.

So, BC = x.

Then, BE = EC =x 2 - As AB || FE.

Therefore, ∠1 = ∠4 ------(1)**[Alternate angles.]**

∠2 = ∠3 ------(2)**[Alternate angles.]** - Since, ∠1 = ∠2
**[AE is the bisector of ∠A.]**

By comparing (1), we get: ∠2 = ∠4. - Since the two angles are equal, triangle ABE is an isosceles triangle.

Therefore, AB = BE =

= 6 cmx 2

⇒ x = 12 cm

⇒ AD = 12 cm. - This means the length of side AD is 12 cm.