Question 416260

A quadrilateral is a parallelogram if and {{{only}}} if the {{{diagonals}}} bisect each other. 

You will have to apply {{{triangle}}}{{{ congruency}}} here.

Consider the two {{{opposite}}} triangles made by the diagonal;they are congruent by {{{SAS}}} congruency since two sides which were bisected were equal and the interior opposite angles made by the diagonals.

Now proving {{{both}}} the set of opposite {{{triangles}}}{{{ congruent}}} you will get {{{opposite}}}{{{ sides}}}{{{ equal}}} which is {{{enough}}} to prove that the {{{quadrilateral}}} is a {{{parallelogram}}}.