Question

Which of the following are true?

i) All squares are rhombuses.

ii) All parallelograms are rectangles.

iii) All rhombuses are kites.

iv) All squares are rectangles.

• A. ii, iii
• B. i, ii
• C. i, iii, iv
• D. None of these

Answer 1

The correct option is C

i, iii, iv

Rhombus has equal sides and their diagonals bisect each other at ${90}^{\circ }$. Square also satisfies these conditions. So, (i) is true.

A rectangle has all angles equal to ${90}^{\circ }$ This is not the case with parallelograms. So, (ii) is false.

A kite has two pairs of equal adjacent sides, one diagonal bisecting other and one pair of equal interior opposite angles. Rhombus satisfies all of these conditions. So, (iii) is true.

Rectangle has all angles as ${90}^{\circ }$and equal opposite sides. Square also has all angles as ${90}^{\circ }$ and all equal sides, hence equal opposite sides. So, (iv) is true.