Given three fixed line segments, find a fourth line segment so that the resulting quadrilateral formed by the…

Do the angle bisectors of the opposite sides of an inscribed quadrilateral meet at right angles?

Explore the paths of four dogs who each start moving from a different vertex of a square.

Fold a sheet of paper into three equal areas.

Find the inscribed rectangle with maximum area for a given triangle.

Find inscribed squares for a given triangle.

Cut a square cake into n pieces so that all the pieces have equal amounts of cake and…

Cut various quadrilaterals into equal portions.

Explore the sequence of square numbers.

Explore relationships of parallelograms with angle bisectors.