Supplementary Investigation 13

Tessellations Based on Rotations & Quadrilaterals

Tool(s) Geometers Sketchpad

Data File(s) si13
Focus Any quadrilateral ABCD will tessellate the plane. Adjoining objects have the same side length but are rotated 180 degrees about their segment midpoints.

Tasks

1. Move vertices A, B, C, and D. Describe the effect on the tessellation.

2. Explain why any quadrilateral will tessellate the plane.

3. Argue that any two triangles with one pair of congruent sides will tessellate the plane.

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