IM 8.9.2 Lesson: Regular Tessellations
For each shape (triangle, square, pentagon, hexagon, and octagon), decide if you can use that shape to make a regular tessellation of the plane. Explain your reasoning.
For the polygons that do not work what goes wrong? Explain your reasoning.
What is the measure of each angle in an equilateral triangle? How do you know?
How many triangles can you fit together at one vertex? Explain why there is no space between the triangles.
Explain why you can continue the pattern of triangles to tessellate the plane.
How can you use your triangular tessellation of the plane to show that regular hexagons can be used to give a regular tessellation of the plane?
Can you make a regular tessellation of the plane using regular polygons with 7 sides?
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[/img]
Can you make a regular tessellation of the plane using regular polygons:
with 9 sides? Explain. (Use the applet above to help your thinking)
What about 10 sides? Explain. (Use the applet above to help your thinking)
What about 11 sides? Explain. (Use the applet above to help your thinking)
What about 12 sides? Explain. (Use the applet above to help your thinking)
How does the measure of each angle in a square compare to the measure of each angle in an equilateral triangle?
How does the measure of each angle in a regular 8-sided polygon compare to the measure of each angle in a regular 7-sided polygon?
What happens to the angles in a regular polygon as you add more sides?
Which polygons can be used to make regular tessellations of the plane?