Question 233169
If it is a parallelogram, then the opposite sides are equal.
If the diagonals are also equal, then you have 4 congruent triangles.


to show you what i mean, let the parallelogram be PQRS.


you have:


PQ = SR


PS = QR


PR = SQ


you can break your parallelogram into 4 triangles.


those triangles are:


PRS and RPQ


SPQ and QRS


all these triangles are congruent by SSS as shown in the following diagram.


<img src = "http://theo.x10hosting.com/2014/090408.jpg" alt="$$$" </>


since all these triangles are congruent, then all their corresponding angles are congruent.


this means that angle PSR is congruent to angle RQP is congruent to angle  SPQ is congruent to angle QRS.


this means that all 4 angles of the parallelogram are congruent to each other.


this means that all the angles of the parallelogram are equal to 90 degrees.


since all the angles of a rectangle are equal to each other, this means that the parallelogram is a rectangle.


it hss all 4 angles equal to each other.
it has both diagonals equal to each other.


that's all that you need because that's what defines a rectangle.


here's a definition of a rectangle from the web.


<a href = "http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php" target = "_blank">http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php</a>\