Which of the following statements are true (T) and which are false (F)? In a parallelogram, the diagonals are equal. In a parallelogram, the diagonals bisect each other. In a parallelogram, the diagonals intersect each other at right angles. In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. If all the angles of a quadrilateral are equal, it is a parallelogram. If three sides of a quadrilateral are equa, it is a parallelogram. If three angles of a quadrilateral are equal, it is a parallelogram. If all the sides of a quadrilateral are equal it is a parallelogram

Explanation

(i) False. Diagonals of parallelogram are not necessarily equal.
(ii) True. This is a known property of a parallelogram.
(iii) False. The diagonals of a parallelogram can intersect at any angle.
(iv) False. A quadrilateral can only be called a parallelogram if both pairs of its opposite sides are equal.
(v) True. If all angles are equal, then it means its opposite angles are also equal which is a condition for a quadrilateral to be called parallelogram.
(vi) False. Main condition of parallelogram includes parallelism of the sides.
(vii) False. Both pair of opposite angles should be equal in order for a quadrilateral to be called a parallelogram.
(viii) True. If all sides are equal then, opposite sides are also equal.