# Give reasons for the following :(a) A square can be thought of as a special rectangle.(b) A rectangle can be thought of as a special parallelogram.(c) A square can be thought of as a special rhombus.(d) Squares, rectangles, parallelograms are all quadrilaterals.(e) Square is also a parallelogram.

To do:

We have to give reasons for the given statements.

Solution:

(a) A rectangle is a quadrilateral in which the opposite sides are parallel and equal to each other and all four angles are right angles.

A square is a quadrilateral in which all the sides are equal and all four angles are right angles.

Therefore,

A square can be thought of as a special rectangle.

(b) A parallelogram is a quadrilateral in which the opposite sides are parallel and equal.

A rectangle is a quadrilateral in which the opposite sides are parallel and equal to each other and all four angles are right angles.

Therefore,

A rectangle can be thought of as a special parallelogram.

(c) A rhombus is a quadrilateral that has all four sides equal and opposite sides parallel.

A square is a quadrilateral in which all the sides are equal and all four angles are right angles.

Therefore,

A square can be thought of as a special rhombus.

(d) A polygon with four sides and four vertices is called a quadrilateral.

A rectangle is a quadrilateral in which the opposite sides are parallel and equal to each other and all four angles are right angles.

A square is a quadrilateral in which all the sides are equal and all four angles are right angles.

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal.

Therefore,

Squares, rectangles, parallelograms are all quadrilaterals.

(e) A parallelogram is a quadrilateral in which the opposite sides are parallel and equal.

A square is a quadrilateral in which all the sides are equal and all four angles are right angles.

Therefore,

Square is also a parallelogram.

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