In parallelogram ABCD, segment BK is the bisector of angle B and point K lies on the side AD

| March 5, 2021 | education

In parallelogram ABCD, segment BK is the bisector of angle B and point K lies on the side AD, with AK = 7, KD = 23. Find the perimeter of parallelogram ABCD.

In order to solve this problem, you need to know the properties of the parallelogram and carefully study the condition of the problem. Let’s draw or imagine a picture of this situation. In the parallelogram ABCD, the bisector BK divides the AD side into segments AK = 7 and KD = 23, which means the entire side AD = 7 + 23 = 30, the opposite side will also be 30, this is the BC = 30 side.

In triangle ABK there are 2 criss-crossing angles at 2 parallel and secant, so there is an isosceles triangle AB = AK = 7.

But AB = CD = 7, as opposite sides of a parallelogram.

The perimeter of the entire parallelogram will be 30 + 7 + 30 + 7 = 74.

So our answer is 74.



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