Question

Which of the following statements are true and which are false? 

(i) The diagonals of a parallelogram are equal. 

(ii) The diagonals of a rectangle are perpendicular to each other. 

(iii) The diagonals of a rhombus are equal. 

(iv) Every rhombus is a kite. 

(v) Every rectangle is a square. 

(vi) Every square is a parallelogram. 

(vii) Every square is a rhombus. 

(viii) Every rectangle is a parallelogram. 

(ix) Every parallelogram is a rectangle. 

(x) Every rhombus is a parallelogram.

Answer 1

(i) False 

Diagonals of parallelogram bisects each other. 

(ii) False 

Diagonals of rectangle do not intersect at right angle. So, they are not perpendicular to each other. 

(iii) False 

Diagonals of rhombus bisect each other. If it’s all sides are equal then only diagonals will be equal and it will be a square. 

(iv) False 

All kites are rhombus but every rhombus is not a kite. 

(v) False 

In square all sides are equal. Length of sides may vary in case of rectangle. 

(vi) True 

In Parallelogram, opposite sides and opposite angles are equal. In square all sides are equal and all angles are right angles. 

(vii) True 

All sides are equal and diagonals bisect each other. 

(viii) True 

Opposite sides and opposite angles are equal. 

(ix) False 

Rectangle forms right angle between adjacent sides but it is not necessary for every parallelogram. 

(x) True 

Opposite sides and opposite angles are equal.