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Question
Complete the following statement by means of one of those given in brackets against each:
If one angle of a parallelogram is a right angle, then it is necessarily a .................
Options
rectangle
square
rhombus
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Solution
If one angle of a parallelogram is a right angle, then it is necessarily a rectangle.
Reason:
Let ABCD be the given parallelogram.
We have, ∠A = 90°
In a parallelogram, opposite angles are equal.
Therefore,
∠C = 90°
Similarly,
∠A + ∠D = 180°
90° + ∠D = 180°
∠D = 90°
Also, ∠B = 90°
Thus, a parallelogram with all the angles being right angle and opposite sides being equal is a rectangle.
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