Question

I will prove that quadrilateral MNOP is a rectangle by demonstrating that both pairs of opposite sides are parallel. slope of MN = _
slope of NO = _
slope of OP = _
slope of PM = _
The slopes of any pair of sides are _.
That being the case, those sides are _.
Therefore, the quadrilateral is a _.

Answer 1

I don't have the coordinates from your diagram, but the general completions are:

slope of MN = slope of OP
slope of NO = slope of PM
The slopes of any pair of opposite sides are equal.
That being the case, those sides are parallel.
Therefore, the quadrilateral is a parallelogram.

Note: Showing both pairs of opposite sides are parallel proves a parallelogram, not automatically a rectangle. To conclude MNOP is a rectangle you also need to show one angle is a right angle (for example slope(MN) · slope(NO) = −1). If you give the coordinates of M, N, O, P I can compute the slopes and finish the proof.