Question

If we wanted to prove quadrilateral MNOP was a parallelogram, which method below would not work?

1. Doing four slope formulas to show both pairs of opposite sides are parallel.


2. Doing two midpoint formulas to show the diagonals intersect at the same point.


3. Doing two slope formulas and two distance formulas to prove the same pair of opposite sides is congruent and parallel.


4. Doing two distance formulas to show that adjacent sides are not the same length

Answer 1

The correct option is 4.

4) Doing two distance formulas to show that adjacent sides are not the same length.

Explanation:

Parallelogram is a quadrilateral which has opposite sides equals and parallel. Example of a parallelogram are rhombus, rectangle, square etc.

We can prove that a quadrilateral MNOP is a parallelogram. If we find the slopes of all four sides and compare those of the opposite ends, same slopes would indicate the opposite sides are parallel, hence the quarilateral is a parallelogram. We can also find the distance of two opposing sides, and slopes of twp opposing sides to determine whether it is a parallelogram or not. The most difficult approach is that diagonals bisect each other at same point.

However, using only two distance formulas will not give us enough information to determine whether a side is parallel or not.