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.

Equal Portions

Cut various quadrilaterals into equal portions.

Square Numbers

Explore the sequence of square numbers.

Angle Bisector

Explore relationships of parallelograms with angle bisectors.


Tile a square patio with square tiles.


Explore transformations of quadrilaterals.

Exploring Rectangle Properties

Draw different rectangles and explore what happens when you change their properties.

Dividing a Rectangle

Divide a rectangle into three triangular regions.

Spiraling Rectangle

Find the area of the given rectangle.

Double Trouble

Construct a square that has twice the perimeter as another square.

Triangles in a Trapezoid

Determine the relationships between the areas of triangles formed by the diagonals of a trapezoid.

Slicing a Parallelogram

Explore the relationships of line segments when the area of a parallelogram is halved.

Area Formulas

Explore the similarity of the area formulas for quadrilaterals and triangles.

Table Arrangement

Explore seating arrangements using square tables.

Interior Angles

Explore the sum of interior angles of a quadrilateral.

Integral Sides

Explore area and perimeter of quadrilaterals whose sides have integral length.

Overlapping Squares

Make more squares from less.

Perplexing Pentominoes

Explore with pentominoes.

Leaving Squares

Remove toothpicks from the figure to leave five squares.

Shaded Squares

Determine the number of “outside” squares in a given figure.


Explore various relationships in a given construction involving a parallelogram.

Quadrilaterals Inscribed Inside Polygons

How many quadrilaterals can be constructed using the vertices of polygons?

Constructing Quadrilaterals 3

Given certain quadrilaterals, construct other quadrilaterals with similar properties.

Quadrilateral Conjectures

Make conjectures about properties of quadrilaterals and provide examples or counterexamples.

Constructing Quadrilaterals 2

Given various properties, determine whether a quadrilateral exists.