Puzzles & Experiments
Experiment #1 Discovering Special Properties of Special Parallelograms
Experiment #2 Midsegment Conjectures
Experiment #3 Quadrilateral Linkages
Experiment #4 Polygon Sum Conjectures
1. Draw a polygon onto a sheet of heaby paper. Cut the polygon and tear off its angles. On another sheet of paper, draw a line and a point on the line. Arrange the torn off angles around the point. Write a paragraph that explains how this activity demonstrates the Polygon Sum Conjecture for this polygon.
2. Draw several polygons that have four or more sides. In each, draw diagonals from a single vertex. Explain how the Polygon Sum Conjecture follows logically from the Triangle Sum Conjecture. Does the Polygon Sum Conjecture apply to concave polygons?
3. On a sphere, investigate the Polygon Sum Conjecture. Once you make a conjecture, explain how it is related to the Triangle Sum Conjecture on a sphere. Be sure to test your conjecture on the smallest and largest possible polygons.
"Discovering Geometry: An Inductive Approach" Serra, P. 281
Experiment #5 Straight Lines - The Parallelogram Pencil Box
Experiment #6 Simple Shapes - Magic Wallet & Pentominoes
Experiment #7 Quadrilaterals in Tangrams