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Question
P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. If AD = 10 cm, then CD =
Options
5 cm
6 cm
8 cm
10 cm
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Solution
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).
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