Midpoints of the Sides of a Quadrilateral

The Activity Problem

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







Conjecture

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





Hint

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, C, or D to realize that each two opposite angles of the figure EFGH, which is formed by joining the midpoints of the adjacent sides of the quadrilateral ABCD, are equal in measure.