Inscribing Regular Polygons
Aligned to G-CO.D.13 — Common Core State Standards for Mathematics.
What this lesson teaches
An equilateral triangle, square, and regular hexagon can each be inscribed in a circle using compass and straightedge. The hexagon is special: the radius of the circle equals the length of each side, so stepping the radius around the circle marks six vertices.
Worked example
Inscribe a regular hexagon in a circle of radius r. Keep the compass set to r. Start at any point on the circle and mark an arc of radius r to find the next vertex; repeat around the circle. Because a chord equal to the radius subtends a 60° central angle, and 360/60 = 6, you land exactly back at the start after six steps, giving six equally spaced vertices of a regular hexagon.
Practice questions
- Why does setting the compass to the circle's radius produce exactly six hexagon vertices?
- To inscribe a square, you first draw two perpendicular diameters. Why do their four endpoints form a square?
- Connecting every other vertex of an inscribed regular hexagon gives what regular polygon?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Inscribir polígonos regulares
Un triángulo equilátero, un cuadrado y un hexágono regular pueden inscribirse en un círculo con compás y regla. El hexágono es especial: el radio del círculo es igual a la longitud de cada lado, así que marcar el radio alrededor del círculo señala seis vértices.
Ejemplo: Inscribe un hexágono regular en un círculo de radio r. Mantén el compás abierto en r. Empieza en cualquier punto del círculo y marca un arco de radio r para hallar el siguiente vértice; repite alrededor del círculo. Como una cuerda igual al radio subtiende un ángulo central de 60°, y 360/60 = 6, regresas exactamente al inicio tras seis pasos, dando seis vértices igualmente espaciados de un hexágono regular.
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