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If a pair of opposite sides of a quadrilateral are equal, then its diagonals are ___________..

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Solution

Given:
A pair of opposite sides of a quadrilateral ABCD are equal.
i.e., AB = CD and AD = BD

Then, the quadrilateral can be a parallelogram, a rectangle, rhombus or a square.
In all the cases the diagonals bisects each other.

Hence, its diagonals are bisecting.

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Similar questions

If a pair of opposite sides of a cylic quadrilateral are equal, prove that its diagonals are equal. [3 MARKS]

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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