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additional investigations

PROPERTIES of Quadrilaterals

Constructing Quadrilaterals 2: Given various properties, determine whether a quadrilateral exists.

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

Constructing Quadrilaterals 3: Given certain quadrilaterals, construct other quadrilaterals with similar properties.

Quadrilaterals Inscribed Inside Polygons: How many quadrilaterals can be constructed using the vertices of polygons?

Relationships: Explore various relationships in a given construction involving a parallelogram.

Shaded Squares: Determine the number of "outside" squares in a given figure.

Leaving Squares: Remove toothpicks from the figure to leave five squares.

Perplexing Pentominoes: Explore with pentominoes.

Overlapping Squares: Make more squares from less.

AREA and PERIMETER of Quadrilaterals

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

Interior Angles: Explore the sum of interior angles of a quadrilateral.

Table Arrangement: Explore seating arrangements using square tables.

Area Formulas: Explore the similarity of the area formulas for quadrilaterals and triangles.

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

Triangles in a Trapezoid: Determine the relationships between the areas of triangles formed by the diagonals of a trapezoid.

Double Trouble: Construct a square that has twice the perimeter as another square.

Spiraling Rectangle: Find the area of the given rectangle.

Dividing a Rectangle: Divide a rectangle into three triangular regions.

Exploring Rectangle Properties:
Draw different rectangles and explore what happens when you change their properties.

SYMMETRY and SIMILARITY of Quadrilaterals

Transformations: Explore transformations of quadrilaterals.

Tiling: Tile a square patio with square tiles.

Angle Bisector: Explore relationships of parallelograms with angle bisectors.

Square Numbers: Explore the sequence of square numbers.

Equal Portions: Cut various quadrilaterals into equal portions.

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.

Inscribed Square: Find inscribed squares for a given triangle.

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

Paper Folding: Fold a sheet of paper into three equal areas.

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

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

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.

Quadrilateral with Maximum Area: Find a quadrilateral with maximum area given a fixed angle and two fixed line segments.

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.

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