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

Answer 1

 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.