Lesson 3Tessellating Polygons

Learning Goal

Let’s make tessellations with different polygons.

Activity 1: Triangle Tessellations

Problem 1

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.

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Your teacher will assign you one of the three triangles. You can use the picture to draw copies of the triangle on tracing paper. Your goal is to find a tessellation of the plane with copies of the triangle.

request a tactile. Three triangles. An acute triangle, a right triangle, and an obtuse triangle.

Activity 2: Quadrilateral Tessellations

Problem 1

Three quadrilaterals - a green and yellow one and a blue trapezoid.

Can you make a tessellation of the plane with copies of the trapezoid? Explain.

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Three quadrilaterals - a green and yellow one and a blue trapezoid.

Can you make a tessellation of the plane with copies of the trapezoid? Explain.

Problem 2

Choose one of the other two quadrilaterals. Next, rotate the quadrilateral 180 degrees around the midpoint of each side. What do you notice?

Problem 3

Can you make a tessellation of the plane with copies of the quadrilateral from the previous problem? Explain your reasoning.

Activity 3: Pentagonal Tessellations

Problem 1

A pentagon with point A being 120 degrees. Other angles are 100, 120, 120, and 80.

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

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    Pause your work here.

  2. 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.

  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).

Print Version
A pentagon with point A being 120 degrees. Other angles are 100, 120, 120, and 80.

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

    Pause your work here.

  2. 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.

  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).