Question

State with reasons whether the following statements are ‘true’ or ‘false’.

(i) Every parallelogram is a rhombus.

(ii) Every rhombus is a rectangle.

(iii) Every rectangle is a parallelogram.

(iv) Every squre is a rectangle.

(v) Every square is a rhombus.

(vi) Every parallelogram is a rectangle.

Answer 1

(i) Every parallelogram is a rhombus.
False, every rhombus is a paralellogram but the vice versa is not true.

(ii) Every rhombus is a rectangle.
False, as in a rectangle all the angles are right angles but the same is not true in a rhombus.

(iii) Every rectangle is a parallelogram.
True, all rectangle have the opposite pair of sides congruent and parallel and the diagonals bisect each other.

(iv) Every square is a rectangle.
True, as all the angles are right angles and the diagonals are congruent to each other.

(v) Every square is a rhombus.
True, as the diagonals of a rhombus are perpendicular bisectors of each other and they also bisect the pair of opposite angles.

(vi) Every parallelogram is a rectangle.
False, as in a parallelogram the opposite angles are congruent but not right angles.