A quadrilateral ABCD is a parallelogram if and only
if(1) Its diagonals are perpendicular(2) Its diagonals bisect each other(3) One pair of its opposite sides is parallel(4) One pair of its opposite angles is equal

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Solution

Quadrilateral is parallelogram if their diagonals are perpendicular to each other.

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Similar questions

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.

If a quadrilateral ABCD is a parallelogram then

Which of the following statements are true or false for a rectangle?

(i) It has two pairs of equal opposite sides.

(ii) It has all its sides of equal length.

(iii) Its diagonals are equal.

(iv) Its diagonals bisect each other.

(v) Its diagonals are perpendicular to each other.

90^{\circ}

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