Construction and Loci

Task goals

• Identify the four base loci (circle, pair of parallel lines, perpendicular bisector, angle bisector) from a plain-language distance condition.
• Construct the perpendicular bisector of a segment using equal-radius compass arcs from both endpoints.
• Construct the bisector of an angle using compass arcs from the vertex and from the two arms.
• Describe or shade a region defined by an inequality version of a locus (e.g. "within" or "closer than" a given distance).
• Solve a compound locus problem by drawing two loci separately and reading off their intersection point(s), including reasoning about how many solutions are possible.
• Explain why a point on a perpendicular bisector or angle bisector satisfies the equidistant condition, using the compass-arc construction as justification.