Your knowledge of constructions from the previous topics will help you in this topic, when we will be completing constructions involving circles. In this topic, you will be using your compass, straightedge and circles to construct equilateral triangles, squares and a regular hexagon.

Essential Questions

• How can you use a compass and straightedge to construct a regular hexagon, a square, and an equilateral triangle inscribed in a circle?

Warm-Up

Before you explore constructions involving figures inscribed in circles, reflect on the constructions you have already learned. Write a two-to-three sentence description for each of the following:

1. congruent segment to a given segment;
2. perpendicular bisector;
3. a perpendicular to a given line that passes through a point not on the line;
4. a perpendicular to a given line that passes through a point on the line;
5. angle bisector;
6. congruent angle to a given angle; and
7. a line parallel to a given line that passes through a given point not on the given line.