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 1 | Hint 2

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

If the slopes of two lines are equal then the two lines are parallel.

 Please enable Java for an interactive construction (with Cinderella).
Drag free points A, B, C, or D to realize that the slopes of each two opposite sides of the figure EFGH, which is formed by joining the midpoints of the adjacent sides of the quadrilateral ABCD, are equal.