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Question

# If one angle of a parallelogram is 900 and its adjacent sides are equal, it is a

A

Square

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B

Rhombus

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C

Rectangle

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D

Trapezium

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Solution

## The correct option is A Square Consider a parallelogram ABCD Given that, one angle of a parallelogram is 900 and its adjacent sides are equal. i.e., ∠A=900,AB=AD If ∠A=900⇒∠B=900 [Opposite angles of parallelogram are equal] Also, ∠A+∠B=1800 [Adjacent angles are supplementary] ⇒∠B=900 ⇒∠D=900 [Opposite angles of parallelogram are equal] AB=AD [Given] AB=CD and AD=BC [Opposite sides of parallelogram are equal] ⇒ All the angles and all the sides are equal in parallelogram ABCD ⇒ABCD is a square.

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