Lesson 4

This lesson allows students to determine a process for constructing an equilateral triangle by finding the possible shapes within the construction of a regular hexagon. There is an opportunity to practice polygon vocabulary beyond equilateral triangles during the first activity. Students continue to practice straightedge and compass construction techniques as well as justify claims involving distance. Students make arguments and critique the reasoning of others when discussing claims about distance using circles (MP3).

One conjecture that builds toward subsequent lessons on proof via rigid motion is using rotation by 120 degrees to show that the equilateral triangle construction produces a triangle with all angles congruent and all sides congruent. Students are introduced to the word inscribed to describe a situation where a polygon sits inside a circle with all the vertices on the circle.

If students have ready access to digital materials in class, they can choose to perform all construction activities with the GeoGebra Construction tool accessible in the Math Tools or available at https://www.geogebra.org/m/VQ57WNyR.