Supplementary Investigation 14

Tessellations Based on Parallelograms and Glide Reflections

Tool(s) Geometers Sketchpad

Data File(s) si14 & si14a

Focus A curve is defined from the endpoint, A, to the midpoint, M, of side AB of parallelogram ABEN. This curve is extended over the second half of the side, MB, using a glide reflection. The entire curve from A to B is then reflected in the perpendicular bisector of BD and translated downward to connect N and E. A second curve is drawn from A to N and translated downward to connect B and E. The same curve is reflected in the perpendicular bisector of BD and translated downward to connect N and B. The resulting object tessellates the plane.

Tasks

1. The figure in si14 (above) was designed to suggest puppies. Adjust the vertices and scales to suggest a cat or some other creature.

2. Measure the area and perimeter of the two "puppies" in si14a (below) with vertices around their boundaries. Are they the same size and shape? Discuss your findings.

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