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tessellating a plane

The blue parallelogram ABCD shown below has been tessellated so that it tiles a surface without any gaps or overlaps. Name as many other quadrilaterals as you can that will also tessellate a flat surface. Explain your solution.

View a Geometer's SketchPad template or a java applet of this construction to convince yourself.



Name as many other individual polygons as you can that will tessellate a flat surface. Justify your answer(s).

What combination(s) of polygons can tessellate a flat surface? Explain why this combination (or these combinations) work while others do not.

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