## 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.

## Quadrilateral with Maximum Area

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

## Maximum Quadrilateral

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

## Inscribed Quadrilateral

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.