In order to identify a quadrilateral as a parallelogram, you must demonstrate that opposite sides of the quadrilateral are parallel. Parallel lines have identical slopes. Given the coordinates of the vertices, you can use the slope formula to calculate the slope of the lines containing each of the four sides of the quadrilateral. If two of the sides have equal slopes and the other two sides also have equal slopes, then the quadrilateral is a parallelogram, otherwise not.
The slope formula is:
where and are the coordinates of the given points.
John
My calculator said it, I believe it, that settles it
