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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 intersect 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.



Answer -

(i) Statement: In a parallelogram, the diagonals are equal.
False
(ii) Statement: In a parallelogram, the diagonals bisect each other.
True
(iii) Statement: In a parallelogram, the diagonals intersect each other at right angles.
False
(iv) Statement: In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.
False
(v) Statement: If all the angles of a quadrilateral are equal, then it is a parallelogram.
True
(vi) Statement: If three sides of a quadrilateral are equal, then it is not necessarily a parallelogram.
False
(vii) Statement: If three angles of a quadrilateral are equal, then it is no necessarily a parallelogram.
False
(viii) Statement: If all sides of a quadrilateral are equal, then it is a parallelogram.
True

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