Give reasons for the following a A square can be thought of as a special rectangle b A rectangle can...

Question

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

Accepted Answer

a A rectangle in which all the interior angles are of same measure ie 90 and only opposite sides of the rectangle are of same length whereas in square all the interior angles are of 90 and all the sides of the square are of same length Hence a rectangle with all sides equal becomes a square Therefore square is a special rectangle b In a parallelogram opposite sides are parallel and equal In a rectangle opposite sides are parallel and equal The interior angles of the rectangle are of same measure ie 90 Hence a parallelogram with each angle as right angle becomes a square Therefore a rectangle is a special parallelogram c All sides of a rhombus and square are equal but in case of square all interior angles are of 90 A rhombus with each angle as right angle becomes a square Therefore a square is a special rhombus d Since all are closed figures with 4 line segments Hence all are quadrilaterals e Opposite sides of a parallelogram are equal and parallel whereas in a square opposite sides are parallel and all 4 sides are of same length Therefore a square is a special parallelogram

NCERT Solutions Class 6 Mathematics Solutions for Exercise 5.7 in Chapter 5 - Understanding Elementary Shapes