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.
(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.