Mathematics — first biennium · Lesson
An angle bisector divides an angle into two equal angles. The construction uses one arc from the vertex and equal-radius arcs from the points obtained on the sides.
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: The first arc locates two points equally distant from the vertex; the next equal-radius arcs determine the bisector direction.
You can already assume: Angles, segments and congruence criteria.
Compass-and-straightedge construction of an angle bisector.
Completed exercises: 0/5 · Correct on first attempt: 0
The first arc locates two points equally distant from the vertex; the next equal-radius arcs determine the bisector direction.
Data / situation: Construct an angle bisector 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.