Which of the following statements are true for a rhombus?

Question:

Which of the following statements are true for a rhombus?

(i) It has two pairs of parallel sides.

(ii) It has two pairs of equal sides.

(iii) It has only two pairs of equal sides.

(iv) Two of its angles are at right angles.

(v) Its diagonals bisect each other at right angles.

(vi) Its diagonals are equal and perpendicular.

(vii) It has all its sides of equal lengths.

(viii) It is a parallelogram.

(ix) It is a quadrilateral.

(x) It can be a square.

(xi) It is a square.

Solution:

(i) True

(ii) True

(iii) True

(iv) False

(v) True

(vi) False

Diagonals of a rhombus are perpendicular, but not equal.

(vii) True

(viii) True

It is a parallelogram because it has two pairs of parallel sides.

(ix) True

It is a quadrilateral because it has four sides.

(x) True

It can be a square if each of the angle is a right angle.

(xi) False

It is not a square because each of the angle is a right angle in a square.

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