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. 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. Students continue to practice straightedge and compass construction techniques and to justify claims involving distance. Students make arguments and critique the reasoning of others when discussing claims about distance using circles (MP3).

If students have ready access to digital materials in class, they can choose to perform all construction activities with the GeoGebra Constructions Tool accessible in the Math Tools or available at https://im612.org/construction-tool.