Lesson 3

Tessellating Polygons

Let’s make tessellations with different polygons.

3.1: Triangle Tessellations

Your teacher will assign you one of the three triangles. Your goal is to find a tessellation of the plane with copies of the triangle.

3.2: Quadrilateral Tessellations

Three quadrilaterals.  Please ask for assistance.
  1. Can you make a tessellation of the plane with copies of the trapezoid? Explain.

  2. Choose one of the other two quadrilaterals. Next, rotate the quadrilateral 180 degrees around the midpoint of each side. What do you notice?
  3. Can you make a tessellation of the plane with copies of the quadrilateral from the previous problem? Explain your reasoning.

3.3: Pentagonal Tessellations

  1. Can you tessellate the plane with copies of the pentagon? Explain. Note that the two sides making angle \(A \) are congruent.

    An irregular pentagon. Angle A measures 120 degrees.  From there, clockwise, the angles measure 100 degrees, 120 degrees, 120 degrees, 80 degrees.

    Pause your work here. 

  2. Take one pentagon and rotate it 120 degrees clockwise about the vertex at angle \(A\), and trace the new pentagon. Next, rotate the pentagon 240 degrees clockwise about the vertex at angle \(A\), and trace the new pentagon.

  3. Explain why the three pentagons make a full circle at the central vertex.

  4. Explain why the shape that the three pentagons make is a hexagon (that is, the sides that look like they are straight really are straight).

Summary