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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a compass and straightedge to place equally spaced points on a circle and connect them accurately. They use circle radii, perpendicular diameters, and repeated chords to justify each construction.
What Mastery Looks Like
- A student creates accurate figures with every vertex on the circle and all required sides congruent. They use perpendicular diameters for the square, radius-length chords for the hexagon, and alternate hexagon vertices for the triangle. They can explain why each method works.
Common Misconceptions
- Students may place vertices by eye or measure angles with a protractor instead of using construction steps. They may draw polygons outside the circle, change the compass width while stepping off a hexagon, or assume equal-looking sides are congruent.
How to Assess It
- Give students three circles with marked centers. Ask them to construct the three required polygons using only a compass and straightedge, leaving all construction marks visible.
Lesson moves
Ways to Teach It
Give pairs three paper circles, compasses, and straightedges; they construct each polygon, then verify equal sides with the compass.
Ask students to explain why stepping one radius around a circle creates six equal chords and how alternate vertices form a triangle.
Run a construction relay where teams draw one justified step at a time, then check that every vertex lies on the circle.
Have students design a circular tile or clock face containing all three polygons and label the central angles.
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Printable HSG-CO.D.13 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-CO.D.13, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSG-CO.D.12
Basic compass and straightedge skills, especially copying lengths and making perpendiculars, support constructing regular polygons inside a circle.
- CCSS.Math.Content.HSG-CO.A.1
Precise meanings of circle, segment, and angle support constructing and justifying equal chords and vertices on the circle.
- CCSS.Math.Content.7.G.A.2
Drawing shapes from given side and angle conditions supports planning exact constructions of regular polygons that meet circle constraints.
Keep exploring
Related Standards
- CCSS.Math.Content.2.G.A.1
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pe...
- CCSS.Math.Content.HSG-C.A.3
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
- CCSS.Math.Content.1.G.A.2
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectang...
- CCSS.Math.Content.K.G.A
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
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