**Understanding Elementary Shapes **

## Exercise – 5.7

**Ex 5.7 Question 1.**

**Say True or False:**

**(a) Each angle of a rectangle is a right angle.**

**(b) The opposite sides of a rectangle are equal in length.**

**(c) The diagonals of a square are perpendicular to one another.**

**(d) All the sides of a rhombus are of equal length.**

**(e) All the sides of a parallelogram are of equal length.**

**(f) The opposite sides of a trapezium are parallel.**

**Solution:**

(a) True

(b) True

(c) True

(d) True

(e) False

(f) False

**Ex 5.7 Question 2.**

**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) Square, rectangles, parallelograms are all quadrilaterals.**

**(e) Square is also a parallelogram.**

**Solution:**

(a) All the angles of the square are right angles and the opposite sides are equal. Therefore square is a special rectangle.

(b) All the opposite sides of the rectangle are equal and parallel. Therefore the rectangle is a special parallelogram.

(c) Yes, because square four sides are equal and diagonals are perpendicular to each other.

(d) Square, rectangles, and parallelograms are all quadrilaterals because all of them have four sides.

(e) All the opposite sides of the square are equal and parallel.

**Ex 5.7 Question 3.**

**A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?**

**Solution:**

A square is only the regular quadrilateral because all the interior angles are of 90^{0} and all sides are of the same length.