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Question

# Which of the following statements are true (T) and which are false (F) ? (i) In a parallelogram, the diagonals are equal. (ii) In a parallelogram, the diagonals bisect each other. (iii) In a parallelogram, the diagonals bisect each other at right angles. (iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. (v) If all the angles of a quadrilateral are equal, it is a parallelogram. (vi) If three sides of a quadrilateral are equal, it is a parallelogram. (vii) If three angles of a quadrilateral are equal, it is a parallelogram (viii) If all the sides of a quadrilateral are equal it is a parallelogram.

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Solution

## (i) False, Diagonals of a parallelogram are not equal. (ii) True. (iii) False, Diagonals bisect each other at right angles in a rhombus or a square only. (iv) False, In a quadrilateral, if opposite sides are equal and parallel, then it is a ||gm. (v) False, If all angles are equal, then it is a square or a rectangle. (vi) False, If opposite sides are equal and parallel then it is a ||gm. (vii) False, If opposite angles are equal, then it is a parallelogram. (viii) False, If all the sides are equal then it is a square or a rhombus but not parallelogram.

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