Prove that ABCD is not a parallelogram. Can someone help me explain how would I prove this because I'm confused?

Hi GAMEMASTERX40! 

We know that parallelograms have two pairs of parallel sides. So lets see if AB is parallel to DC.  One way of finding sets of parallel lines is if the slopes are equal. First for the slope of AB: We can use the coordinate pairs for A and B, (1,1) and (4,6), to find the slope: \(\frac{6-1}{4-1}\), which simplifies to \(\frac{5}{3}.\) Now for the slope of CD: We can again use the coordinate pairs: C=(9,6) and D=(5,1). The slope is 5/4. Clearly 5/4 is not equal to 5/3, so AB is not parallel to CD, and since a parallelogram needs 2 sets of parallel sides, not one, ABCD is not a parallelogram.