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.

AcademicMathematicsNCERTClass 6

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.

raja
Updated on 10-Oct-2022 13:34:43

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