Constructions
Understand the basic straightedge-and-compass constructions of geometry.
Objective
Understand the basic straightedge-and-compass constructions of geometry.
What it means
A construction is a precise geometric drawing made using only a compass and straightedge, without measuring numbers directly.
Key terms
- Compass
- A tool used to draw circles or arcs of a fixed radius.
- Straightedge
- A tool used to draw straight lines, with no measurement marks used.
- Perpendicular bisector
- A line that cuts a segment in half at a 90° angle.
- Angle bisector
- A ray that splits an angle into two congruent angles.
Rules to remember
- To copy a segment, keep the compass width fixed while transferring it.
- To bisect a segment, draw arcs from each endpoint with equal radius greater than half the segment; their intersections define the perpendicular bisector.
- To bisect an angle, draw an arc crossing both rays, then arcs from those points to find the bisecting ray.
Step by step
- 1Set the compassChoose a radius based on the given segment or angle.
- 2Draw arcsSwing arcs from key points so they intersect.
- 3Connect pointsUse the straightedge to connect the intersection points to complete the construction.
Common mistakes
- Using a ruler to measure lengths instead of transferring them with a compass.
- Changing the compass width mid-construction when it should stay fixed.
Tips
- Keep your compass radius larger than half the segment when bisecting, or the arcs won't cross.