Introduction:
A rhombus is a quadrilateral with all sides of equal length. The midpoints of the sides of a rhombus can be joined to form a figure. We need to prove that this figure is a rectangle.

Proof:
Let ABCD be a rhombus, and let E, F, G, and H be the midpoints of the sides AB, BC, CD, and DA respectively.

Step 1: Show that all sides are parallel
To prove that the figure formed by joining the midpoints is a rectangle, we need to show that the opposite sides are parallel.

- Draw diagonal AC, which bisects each other at point O.
- Since ABCD is a rhombus, all sides are equal in length.
- By the midpoint theorem, EO is parallel to AD, and FO is parallel to AB.
- Also, GO is parallel to BC, and HO is parallel to CD.
- Therefore, opposite sides EO and GO are parallel, and FO and HO are parallel.

Step 2: Show that all angles are right angles
To prove that the figure is a rectangle, we need to show that all angles are right angles.

- Since diagonal AC bisects each other at point O, it divides the figure into four triangles: AEO, BFO, CGO, and DHO.
- Since ABCD is a rhombus, all angles are equal to 90 degrees.
- Therefore, angles at E, F, G, and H are all right angles.

Step 3: Conclusion
- We have shown that the opposite sides are parallel and all angles are right angles.
- A quadrilateral with opposite sides parallel and all angles right angles is a rectangle.
- Therefore, the figure formed by joining the midpoints of the sides of a rhombus successively is a rectangle.

Summary:
By proving that the opposite sides are parallel and all angles are right angles, we have shown that the figure formed by joining the midpoints of the sides of a rhombus successively is a rectangle.