Exam 19: Tessellations

A) Explain how you know that every parallelogram will tessellate the plane. Drawing pictures to illustrate your thinking may be helpful. B) Explain how you know that every triangle will tessellate the plane. Drawing pictures to illustrate your thinking may be helpful. C) Explain how you know, without taking the time to draw it out accurately, why a regular pentagon cannot tessellate the plane.

Which shape(s) will tessellate the plane?

State whether each of the following shapes can tessellate the plane. A) a regular pentagon B) a regular hexagon C) D)

Given the following figure, show how to tessellate the plane. Explain how you would know without being able to measure whether it tessellates. Use at least 10 copies, not all in a row.

Which region(s) will tessellate the plane?

State whether each of the following shapes can tessellate the plane. A) a regular 11-gon B) C)

Explain whether a regular pentagon can tessellate the plane. Be very specific, using angles measures. Write the explanation in full, understandable sentences.

Explain why a regular hexagon can tessellate the plane while a regular octagon cannot.

Which item(s) can tessellate space?