prove that a rectangle is a parallelogram.

let ABCD be a rectangle

to prove that it's a parallelogram, we must show that either one pair of opp sides is parallel and equal

or

 both pairs of opp sides are parallel.

angle A=90 degrees

angleD=90 degrees

So,

AB and CD are parallel(int angles on the same side of the transversal are supplementary)

simly,

AC and BD  can be shown parallel.

So ABCD is a parallelogram.

As such,

 the definition of a rectangle is that it's a parallelogram with one angle as  a right angle.