CCSS.Math.Content.HSG-CO.D.13
The standard
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Common Core State Standards for Mathematics
What this standard means
Students need to use a compass and straightedge to build regular polygons inside a given circle. They should know how the circle’s radius helps place equal points around the circle, then connect those points accurately.
Mastery looks like clean constructions with clear compass marks, equal side lengths, and vertices on the circle. Students often get stuck by changing the compass width, guessing by eye, or not understanding why six radius steps make a hexagon and every other point makes a triangle.
Ways to teach it
- Hands-on activity: Give students a circle template, compass, and straightedge, then have them construct a hexagon, triangle, and square on separate circles.
- Discussion prompt: Explain why stepping the radius around a circle creates six equal spaces without measuring angles.
- Quick assessment: Hand students one circle and ask them to construct an inscribed equilateral triangle, leaving all construction marks visible.
- Real-world connection: Show a photo of a tiled floor or logo, then identify where inscribed regular polygons could be used in the design.
Plan a lesson for CCSS.Math.Content.HSG-CO.D.13
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