Deck 19: Tessellations

Question 1

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.

Answer 1

A) You will likely get a drawing.
B) You will likely get a drawing-check that there is a clear, repeatable pattern.
C) Each angle of a regular pentagon has a size of 108°, and 108° angles will not fit together to make 360°.

Question 2

State whether each of the following shapes can tessellate the plane.

A) a regular pentagon
B) a regular hexagon

Answer 2

A) no
B) yes
C) yes
D) yes

Question 3

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

Answer 3

Regular octagons have angles with 145°, and angles of 145° will not fit together to make 360°, whereas regular hexagons have angles with 120°, and angles of 120° will fit together to make 360°.

Question 4

State whether each of the following shapes can tessellate the plane.

A) a regular 11-gon

Question 5

Which region(s) will tessellate the plane?

Question 6

Which shape(s) will tessellate the plane?

A) a regular octagon
B) a regular triangle
C) an obtuse scalene triangle
D) a regular dodecagon
E)

Question 7

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

Question 8

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.

Question 9

Which item(s) can tessellate space?

A) a Cheerios cereal box
B) a baseball
C) a carrot (one size)
D) a CD case