## Constructing a Square

Use a dynamic software tool to construct a square in different ways.

## Quadrilateral with Squares on the Sides

Explore the relationship of the two line segments formed by connecting the centers of the squares on the opposite sides of the quadrilateral.

Find a quadrilateral with maximum area given a fixed angle and two fixed line segments.

Given three fixed line segments, find a fourth line segment so that the resulting quadrilateral formed by the four segments has maximum area.

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

## Four Dogs

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

## Paper Folding

Fold a sheet of paper into three equal areas.

## Inscribed Rectangle

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

## Inscribed Square

Find inscribed squares for a given triangle.

## Cutting the Cake

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