Question 1183621
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

proof:
Given above is parallelogram {{{ABCD}}} and we want to prove the diagonals bisects each other into equal lengths.

First we join the diagonals and where they intersect is point {{{E}}}. 
Angle {{{ECD}}} and {{{EAB }}}are equal ({{{given}}}),  then lines {{{CD}}} and {{{AB}}} are parallel and that makes them alternate angles. 

Angles {{{EDC}}} and {{{EBA}}} are equal in measure for the same reason. 

Line {{{CD}}} and {{{AB}}} are equal in length because opposite sides in a parallelogram are are equal. 

Therefore triangle {{{ABE}}} and {{{CED}}} are congruent because they have 2 angles and a side in common. 

Hence line {{{CE}}} and {{{EB}}} are equal and {{{AE}}} and {{{ED}}} are equal due to congruent triangles.

Therefore the diagonals of a parallelogram do bisect each other into equal parts. 

since

{{{DE+EB =DB}}}
{{{AE+EC=AC}}}
=> diagonals {{{AC=DB}}}

 So, a parallelogram {{{ABCD}}} shown in the image {{{is}}} a {{{rectangle}}}.