Answer
When the midpoints of a parallelogram are connected, they form a rectangle.
Work Step by Step
We name the sides of the rhombus:
$(0,0) ; (2b,2c); (2a+2b, 2c); (2a,0)$
Thus, the midpoints are:
$(b,c); (a+2b, 2c); (2a+b,c); (a,0)$
Plugging these into the distance formula, we find:
$s_1 = \sqrt{c^2 +(b-a)^2} $
$s_2 = \sqrt{c^2 +(-b-a)^2} $
$s_3 = \sqrt{c^2 +(-b-a)^2} $
$s_4 = \sqrt{c^2 +(b-a)^2} $
Since opposite sides are congruent and the angles are 90 degrees, it follows that the shape is a rectangle.
