Learning Focus
Construct perpendicular and parallel lines, inscribed hexagons, and triangle centers.
Big idea
More constructions build on the basics.
- Parallel line: copy a corresponding angle at the new point.
- Regular hexagon: step the radius around a circle six times; side length equals the radius.
- Circumcenter: intersection of the perpendicular bisectors of the sides.
- Incenter: intersection of the angle bisectors.
Worked example
A circle has radius . Starting at a point on the circle, mark off arcs of radius around the circle. Six marks return to the start; joining them gives a regular hexagon.
The center and two adjacent vertices form an equilateral triangle, so each hexagon side is .
Takeaways
- Equal corresponding angles give parallel lines.
- Hexagon side circle radius.
- Triangle centers come from bisectors.