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Question

In a kite shaped figure ABCD, AB=AD and CB=CD. Points P,Q and R are mid-points of sides AB,BC and CD respectively. Then, find PQR

A
45
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B
30
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C
90
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D
60
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Solution

The correct option is C 90
Given: ABCD is a kite shaped figure. AB=AD, BC=CD, P, Q< R are mid points of AB, BC and CD respectively

To Prove: PQR=90

Construction: Join AC and BD
In ABC

P is mid point of AB and Q is mid point of BC

Then, PQAC (By Mid point theorem)
In BCD

Q is mid point of BC and R is mid point of CD

Then, QRBD (mid point theorem)
We know, diagonals of the Kite shaped figure, bisect at right angles.
thus, ACBD

hence, PQQR (Angle made between two lines is same as the angle between their corresponding parallel sides)
or PQR=90

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