Problem preview

G-CO.13 Core M1-036-R02-V02

Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.

Construct an inscribed equilateral triangle from six radius steps

Problem

A circle has center \(P\). Starting at \(G\), its radius is stepped around the circumference to mark \(\text{six}\) points \(G,~H,~J,~K,~L,~\text{and}~M\) in order. Construct an inscribed equilateral triangle by stating the vertices, central spacing, connection sequence, and result.

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vertices = adjacent G,H,J; central spacing = 60°,60°,240°; connection = G-H-J-G; result = equilateral

vertices = all six; central spacing = 60°; connection = all marks; result = triangle

vertices = G,J,M; central spacings = 120°,180°,60°; connection = G-J-M-G; result = equilateral

vertices = alternating G,J,L; central spacing = 120°; connection = G-J-L-G; result = inscribed equilateral triangle

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Curriculum context

Course: Math I
Standard: G-CO.13
Category: Geometry
Domain: Congruence
Objective: Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.
Problem type: Construct an inscribed equilateral triangle from six radius steps