Question

State with reason whether the following statement is ‘True’ or ‘False’. Every rectangle is a parallelogram.
\[\left( {\text{A}} \right){\text{ True}}\]
\[\left( B \right){\text{ False}}\]

Answer 1

Hint:: A quadrilateral is a parallelogram if both pairs of opposite sides are parallel. In a rectangle, each pair of co-interior angles are supplementary because two right angles add to a straight angle. So the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram.

Complete step by step solution:
Parallelograms: A parallelogram is a quadrilateral whose opposite sides are parallel.
Properties of a parallelogram:
The opposite angles of a parallelogram are equal.
The opposite sides of a parallelogram are equal.
The diagonals of a parallelogram bisect each other.

Rectangles: A rectangle is a quadrilateral in which all angles are right angles.
Properties of a rectangle:
The opposite sides of a rectangle are equal.
The diagonals of a rectangle are equal and bisect each other.

Now we know that for any quadrilateral to be a parallelogram, a pair of opposite angles should be congruent. Now have a look at the above diagram. From which we have
\[\angle A = \angle B = \angle C = \angle D = 90^\circ \]
Or we can also say that
\[\angle A = \angle C = 90^\circ \] and \[\angle B = \angle D = 90^\circ \]
That is the opposite angles of a rectangle are equal and also the opposite sides of a rectangle are also equal. Now the rectangle ABCD has all the properties that a parallelogram has. Therefore, we can say that “Every rectangle is a parallelogram”.
Hence the correct option is \[\left( {\text{A}} \right){\text{ True}}\]

Note:
Remember that if one angle of a parallelogram is a right angle then it is a rectangle. Also keep in mind that not all quadrilaterals are parallelograms. Always start by making a drawing for better understanding when proving quadrilateral as a parallelogram.