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| 9.2 Concepts In section 9.2 it is shown that when three angles of a triangle are cut off and placed side by side with the vertices at a point, they form a straight angle with 180º, that is, one-half of a revolution about the point. Experiment with polygons of 4, 5, and 6 sides by cutting off their angles and placing them around a point to see how many revolutions or partial revolutions are made. Then try nonconvex polygons of 4, 5, and 6 sides. Summarize your experimental conclusions and illustrate your results with diagrams. 9.2 Teaching When teachers point out geometric shapes in nature or in architecture, students' awareness of geometry in the environment is increased. NCTM Standards 2000, page 101Make a portfolio (photographs, sketches, magazines, etc.) of geometric shapes from nature and architecture that can be found in your community. Match each shape from nature or architecture to a diagram with the name of the corresponding geometric shape. 9.2 Concepts The following method for tessellating with an arbitrary quadrilateral was suggested by a student. 1. Draw the quadrilateral on a piece of paper. 2. Cut a copy of that quadrilateral from a separate piece of paper. 3. Place the cutout copy on the drawing. 4. Rotate the copy 180º about the midpoint of an edge and trace around the copy. 5. Repeat steps 3 and 4 for all sides of the original drawing. 6. Repeat steps 3 and 4 for all sides of the newly created figures to extend the tessellation. Try this procedure with a convex and a nonconvex quadrilateral. Summarize your results using illustrations and explain why you believe this method works or fails. |