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Quadrilaterals — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsQuadrilaterals1 Mark
MCQ
If $\text{ABCD}$ 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 $\text{ABCD}$ 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, $\angle\text{A}=\angle\text{C}=\angle\text{B}=\angle\text{D}=90^{\circ}$
$\therefore \text{ABCD}$ is a rectangle.

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