Theorems about rhombus and rectangle?

Question

How to prove the theorems:
1)The lines joining the midpoints of opposite sides of rhombus forms a rectangle.
and
2)The lines joining midpoints of opposite sides of rectangle forms a rhombus.

Thank you in advance.

Answer 1

I think you may have this a little wrong. The two lines that join the midpoints of the opposite sides of a rhombus intersect. Ditto for the rectangle. I suspect you want the four lines that join the midpoints of adjacent sides of either the rhombus or rectangle.