Question
Show that a quadrilateral is a parallelogram if an only if diagonals bisect each other.
Solution
(i) Assume that quadrilateral ABCD is a parallelogram.
Let
be the position vectors of A, B, C and D respectively with reference to O as the origin.
Let
be the position vectors of A, B, C and D respectively with reference to O as the origin.∴ P.V. of mid-point of diagonal BD = P.V. of mid-point of diagonal AC.
∴ diagonal AC and BD bisect each other.
(ii) Assume that the diagonals AC and BD of the quadrilateral bisect each other.
∴ P.V. of mid-point of diagonal BD = P.V. of mid-point of diagonal AC.
