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

- Can you make a tessellation of the plane with copies of the trapezoid? Explain.
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Choose one of the other two quadrilaterals. Next, rotate the quadrilateral 180 degrees around the midpoint of each side. What do you notice?
- Can you make a tessellation of the plane with copies of the quadrilateral from the previous problem? Explain your reasoning.
3.3: Pentagonal Tessellations
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Can you tessellate the plane with copies of the pentagon? Explain. Note that the two sides making angle are congruent.
Pause your work here.
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Take one pentagon and rotate it 120 degrees clockwise about the vertex at angle , and trace the new pentagon. Next, rotate the pentagon 240 degrees clockwise about the vertex at angle , and trace the new pentagon.
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Explain why the three pentagons make a full circle at the central vertex.
- 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).