Answer
The segments that connect midpoints for a quadrilateral bisect.
Work Step by Step
We assign coordinates for each point on quadrilateral ABCD:
$A: 0,0 \\ B: 2a, 2b \\ C: 2c, 2d \\ D: 2e, 0$
This means that the midpoints are:
$(a,b); (a+c, b+d); (e,0); (e+c, d)$
We find the midpoint of each line:
$mid_1 = (\frac{a+e+c}{2}, \frac{b+d}{2})$
$mid_2 = (\frac{a+e+c}{2}, \frac{b+d}{2})$
The midpoints are the same, so they bisect each other.
