If you would fill in the blanks, that would really be appreciated!

By applying the slope formula , I find that the slope of segment DE is zero since the difference between the y coordinates  of points D and E  is zero and  any number divided into zero is zero.  The slope of segment AB is also zero  because  (0-0) /(x2-0) =0   Because the two segments have the same slope  they must be parallel  according to the definition of parallel lines.

Step-by-step explanation:

slope formula = (y2-y1)/(x2-x1)

slope for DE = (y1/2-y1/2)/((x1+x2/2 - x1/2)

                      = 0 /(x2/2)

                      = 0

slope for AB = (0-0)/((x1+x2/2 - x1/2)

                      = 0 /(x2-0)

                      = 0/x2

                      =0

Parallel lines have the same slope