EXERCISE 5.7

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 rhombus are of equal length.
(e) All the sides of parallelogram are of equal length.
(f) The opposite sides of a trapezium are parallel.
Ans:
(a) True,   (b) True,  (c) True,   (d) True,   (e) False,   (f) False.

2) Give reasons for the following :
(a) A square can be thought of as a special rectangle.
Ans : A rectangle with all sides equal becomes a square.
(b) A rectangle can be thought as special parallelogram.

Ans : A parallelogram with each angle a right angle becomes a rectangle.
(c) A square can be thought of as special rhombus.

Ans : All sides of rhombus and square are equal but in case of square all interior angles are 90˚.A rhombus with each angle as right angle becomes a square.
(d) Square, rectangle, parallelogram are all quadrilaterals.

Ans : Since, all are closed figures with 4 line segments hence all are quadrilaterals.
(e) Square is also a parallelogram.

Ans : Opposite sides of a square are parallel as in a parallelogram and in addition all sides are equal in a square, hence square is also a parallelogram.

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?
Ans : A square is a ‘regular’ quadrilateral.