Formal Compass Constructions
Aligned to G-CO.D.12 — Common Core State Standards for Mathematics.
What this lesson teaches
Compass-and-straightedge constructions produce exact figures using only equal-radius arcs and straight edges. The perpendicular bisector of a segment is found with two arcs of equal radius from each endpoint. Constructions justify why a figure has a claimed property.
Worked example
Construct the perpendicular bisector of segment AB. Open the compass wider than half of AB. From A, draw an arc above and below the segment; keeping the same opening, from B draw two more arcs crossing them at points P and Q. Draw line PQ. Every point on PQ is equidistant from A and B, so PQ is perpendicular to AB and passes through its midpoint.
Practice questions
- Describe the arcs needed to bisect a given angle with compass and straightedge.
- Why must the compass keep the same radius when drawing the two sets of arcs for a perpendicular bisector?
- To copy a segment of length AB onto a ray, what tool setting guarantees the copy is exactly the same length?
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
Construcciones formales con compás
Las construcciones con compás y regla producen figuras exactas usando solo arcos de igual radio y líneas rectas. La mediatriz de un segmento se halla con dos arcos de igual radio desde cada extremo. Las construcciones justifican por qué una figura tiene una propiedad afirmada.
Ejemplo: Construye la mediatriz del segmento AB. Abre el compás a más de la mitad de AB. Desde A, traza un arco arriba y abajo del segmento; con la misma abertura, desde B traza dos arcos más que los crucen en los puntos P y Q. Traza la recta PQ. Cada punto de PQ equidista de A y B, así que PQ es perpendicular a AB y pasa por su punto medio.
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