Lesson 22

Now What Can You Build?

  • Let’s construct some creative shapes.

22.1: Notice and Wonder: Dramatic Designs

What do you notice? What do you wonder?

A blue equilateral triangle with 3 identical white circles centered atop each midpoint. The circles do not intersect each other and have a diameter about half the side length.
Regular hexagon with center cube made from 3 rhombi. Top and upper left sides of hexagon and lower rhombus are blue.
Regular hexagon formed from a vertical center rectangle and two identical pairs of triangles on each side, rotated 180 degrees. One large right triangle and one small blue obtuse triangle.

22.2: Duplicate a Design

Your teacher will give you a collection of designs that all began from the construction of a regular hexagon. Choose one to use.

  1. Record any rigid motions (rotation, reflection, or translation) you see in your design.
  2. Use straightedge and compass moves to recreate the design.
  3. Write down instructions for how to construct it.

22.3: Make Your Own Design

Use dynamic geometry software to create your own design.

Write down the moves you followed so someone else can recreate your design. 

If you get stuck, consider reviewing all the constructions you have done so far. For an additional challenge, include examples of rigid motions or symmetry in your design.

Construct a tessellation with rotation, reflection, and translation symmetry.

22.4: Make Their Design

  1. Follow the instructions to make a design.
  2. List everything in the design that is congruent. Explain how you know.


There is a deep connection between geometry and art. Using simple construction tools, it’s possible to create beautiful patterns. Precisely recording instructions for a pattern allows other people to make the same pattern and enjoy it for themselves! These same ideas can be applied in three-dimensional space to create the objects we use and appreciate every day.