Mathematics — first biennium · Lesson
A perpendicular bisector is constructed with equal-radius arcs centred at the segment endpoints. Their intersections determine a perpendicular line through the midpoint.
Prerequisites: Angles, segments and congruence criteria
Goal: Construct a perpendicular bisector and angle bisector with compass and straightedge and understand their locus properties.
In this lesson: Construct a perpendicular bisector and angle bisector with compass and straightedge and understand their locus properties.
New concept: In straightedge-and-compass constructions, the result must come from geometric intersections, not from measuring with a ruler. A perpendicular bisector comes from equal-radius arcs centred at the segment endpoints; an angle bisector uses arcs constructed from the angle sides.
How to proceed: Do not estimate the midpoint by eye: use two arcs with the same compass opening and join their intersections.
You can already assume: Angles, segments and congruence criteria.
Compass-and-straightedge construction of a perpendicular bisector.
Completed exercises: 0/5 · Correct on first attempt: 0
Do not estimate the midpoint by eye: use two arcs with the same compass opening and join their intersections.
Data / situation: Construct the perpendicular bisector of segment AB using compass and straightedge.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.