1.

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.

Answer»

(i) It has two pairs of parallel sides.

True, Rhombus is a parallelogram having two pairs of parallel sides.

(ii) It has two pairs of equal sides.

True, Rhombus has two pairs of equal sides .

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

False, Rhombus has all four sides equal.

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

False, rhombus has no angle of right angle.

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

True, in rhombus diagonals bisect each other at right angles.

(vi) Its diagonals are equal and perpendicular.

False, in rhombus diagonals are of unequal length.

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

True, Rhombus has all four sides equal.

(viii) It is a parallelogram.

True, Rhombus is a parallelogram since opposite sides equal and parallel.

(ix) It is a quadrilateral.

True, Rhombus is a quadrilateral since it has four sides.

(x) It can be a square.

True, Rhombus becomes square when any one angle is 90°.

(xi) It is a square.

False, Rhombus is never a square. Since in a square each angle is 90°.



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