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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Answer:

12 cm

Step by Step Explanation:
  2. 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:
  3. Given: Bisector of ∠A bisect line BC into two equal parts.
  4. Let us assume that AD = x.
    So, BC = x.
    Then, BE = EC =  
    x
    2
     
  5. As AB || FE.
    Therefore, ∠1 = ∠4 ------(1)   [Alternate angles.]
    ∠2 = ∠3   ------(2)[Alternate angles.]
  6. Since, ∠1 = ∠2   [AE is the bisector of ∠A.]
    By comparing (1), we get: ∠2 = ∠4.
  7. Since the two angles are equal, triangle ABE is an isosceles triangle.
    Therefore, AB = BE =  
    x
    2
      = 6 cm
    ⇒ x = 12 cm
    ⇒ AD = 12 cm.
  8. This means the length of side AD is 12 cm.

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