If ABCD is a parallelogram with two adjacent angles = then the pa… - Vidyadip

MCQ

If $ABCD$ is a parallelogram with two adjacent angles $\angle\text{A}=\angle\text{B}$ then the parallelogram is a:

A
Rhombus.
B
Trapezium.
✓
Rectangle.
D
None of these.

✓

Answer

Correct option: C.

Rectangle.

Given that $ABCD$ is a parallelogram.
We konw that, opposite sides of a parallelogram are parallel.
$\Rightarrow\angle\text{A}+\angle\text{B}=180^{\circ}$ ...(interior angles)
Also, $\angle\text{A}=\angle\text{B}=90^{\circ} ...($Given$)$
Since opposite angles of a parallelogram are equal,
$\angle\text{A}=\angle\text{C}$ and $\angle\text{B}=\angle\text{D}$
So, $\angle\text{A}=\angle\text{C}=\angle\text{B}=\angle\text{D}=90^{\circ}$
$\therefore ABCD$ is a rectangle.

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