NY Next Generation Math GEO-G.CO.13
The Standard
Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students construct an equilateral triangle, square, and regular hexagon inside a circle. They justify why each construction produces equal sides, required angles, and vertices on the circle.
What Mastery Looks Like
- The student completes each compass-and-straightedge construction accurately and preserves construction marks. The justification links radii, perpendicular bisectors, or repeated arcs to regularity.
Common Misconceptions
- Students may estimate vertex spacing or erase the arcs that justify the construction. They may prove the figure is regular without showing every vertex lies on the circle.
How to Assess It
- Give a blank circle and construction tools. Ask students to inscribe one assigned polygon and write two sentences justifying its side or angle relationships.
Lesson moves
Ways to Teach It
Use compasses and straightedges to inscribe all three polygons on separate paper circles.
Ask why stepping one radius around a circle produces a regular hexagon.
Play construction-order scramble with diagrams and steps for each inscribed polygon.
Design a circular tile or emblem using one justified inscribed construction.
Keep exploring
Related Standards
- NY-7.G.2
Draw triangles when given measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
- GEO-G.SRT.5.b
Prove relationships in geometric figures.
- GEO-G.C.2.a
Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.
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