Question

If one angle of a parallelogram is ${90}^0$ and its adjacent sides are equal, it is a

• A. Square
• B. Rhombus
• C. Rectangle
• D. Trapezium

Answer 1

The correct option is A

Square

Consider a parallelogram $ABCD$

Given that, one angle of a parallelogram is ${90}^0$ and its adjacent sides are equal.

i.e., $\angle A={90}^0,AB=AD$

If $\angle A={90}^0\Rightarrow \angle B={90}^0$ [Opposite angles of parallelogram are equal]

Also, $\angle A+\angle B={180}^0$ [Adjacent angles are supplementary]

$\Rightarrow \angle B={90}^0$

$\Rightarrow \angle D={90}^0$ [Opposite angles of parallelogram are equal]

$AB=AD$ [Given]

$AB=CDandAD=BC$ [Opposite sides of parallelogram are equal]

$\Rightarrow$ All the angles and all the sides are equal in parallelogram $ABCD$

$\Rightarrow ABCD$ is a square.