In a parallelogram ABCD, the bisector of ∠A also bisects the side BC. If AB = 6 cm, find the length of side AD.
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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 =
- 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 cm
⇒ x = 12 cm
⇒ AD = 12 cm.
- This means the length of side AD is 12 cm.