#### Answer

When the midpoints of the sides of a parallelogram are connected, the shape formed is a parallelogram.

#### Work Step by Step

We draw the base of the parallelogram on the x-axis, with a vertex at (0,0). We define the midpoints as follows:
$ B: (b,c) \\ C: (a+2b,2c) \\ D: (2a+b,c) \\E: (a,0)$
We use the equation for slope:
$m = \frac{y_2-y_1}{x_2-x_1}$
We find:
$m_1 = \frac{2c-c}{2b+a-b}=\frac{c}{b+a}$
$m_2 = \frac{2c-c}{a+2b-2a-b}=\frac{b-a}{c}$
$m_3 = \frac{c-0}{2a+b-a}=\frac{c}{b+a}$
$m_4 =\frac{c}{b-a}$
We see that the slopes of opposite sides are equal, making opposite sides parallel and making the shape a parallelogram.