Use a dynamic software tool to construct a square in different ways.
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?
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 equal amounts of frosting.
Cut various quadrilaterals into equal portions.
Explore the sequence of square numbers.
Explore relationships of parallelograms with angle bisectors.
Tile a square patio with square tiles.
Explore transformations of quadrilaterals.
Draw different rectangles and explore what happens when you change their properties.
Divide a rectangle into three triangular regions.
Find the area of the given rectangle.
Construct a square that has twice the perimeter as another square.
Determine the relationships between the areas of triangles formed by the diagonals of a trapezoid.
Explore the relationships of line segments when the area of a parallelogram is halved.
Explore the similarity of the area formulas for quadrilaterals and triangles.
Explore seating arrangements using square tables.
Explore the sum of interior angles of a quadrilateral.
Explore area and perimeter of quadrilaterals whose sides have integral length.
Make more squares from less.
Explore with pentominoes.
Remove toothpicks from the figure to leave five squares.
Determine the number of “outside” squares in a given figure.
Explore various relationships in a given construction involving a parallelogram.
How many quadrilaterals can be constructed using the vertices of polygons?
Given certain quadrilaterals, construct other quadrilaterals with similar properties.
Make conjectures about properties of quadrilaterals and provide examples or counterexamples.
Given various properties, determine whether a quadrilateral exists.