Midpoints of the Sides of a Parallelogram

Proposed Problem 1

What is the figure formed by joining the midpoints of the adjacent sides of a parallelogram?

Conjecture

The figure formed by joinig the midpoints of the sides of a parallelogram is another parallelogram.

Hint 1 | Hint 2

A parallelogram is a quadrilateral, in which each two opposite sides are equal in length.

A parallelogram is a quadrilateral, in which each two opposite angles are equal in measure.

Please enable Java for an interactive construction (with Cinderella).

Drag free points A, B, or C to alter the parallelogram ABCD and observe the length of each two opposite sides of the figure EFGH, which is formed by joining the midpoints of the adjacent sides of the parallelogram ABCD or the measurement of each two opposite angles of the same figure to check the correctness of the made conjecture.