Department of Mathematics Education
EMAT 6600

Quadrilateral with a Square Constructed on Each Side

Given any quadrilateral, construct a square and locate its center on each side of the quadrilateral. Explore the relationship of the two segments defined by connecting the centers of squares on the opposite sides of the quadrilateral.


Conjectures?

Proofs?

Do your conjectures hold if the quadrilateral is not convex? Explore.
Suppose the Quadrilateral is a parallelogram. What additional conjectures and proofs can you find? Consider also a quadrilateral formed by the centers of the four squares.


Return to the EMAT 4600/6600 Page