The middle point of BC is (0,2), the midpoint of CD is (1,0) to prove two lines are parallel, prove their slopes are the same. slope of BD: m=rise/run=4/-2=-2 (the run is negative because to get to B from D on the grid, you have to move from right to left, then upward. If the horizontal move is from left to right, the run is positive) slope of EG: m=rise/run=2/-1=-2 EG and BD have the same slope, so they are parallel.
