Constructions use a compass and straight edge to draw accurate geometric figures. Loci are sets of points that satisfy a given condition.
Key Constructions
Perpendicular Bisector
Bisects a line segment at 90°. Arcs from both endpoints → join intersections.
Locus: all points equidistant from two points.
Angle Bisector
Divides an angle in half. Arc from vertex → arcs from where it cuts the arms → join.
Locus: all points equidistant from two lines.
Perpendicular from a Point to a Line
Arc from the point cuts the line twice → perpendicular bisector of those two intersections.
Constructing Triangles
Given SSS, SAS, or ASA — use ruler, compass, and protractor.
Common Loci
| Condition | Locus |
|---|---|
| Fixed distance from a point | Circle |
| Fixed distance from a line | Parallel lines (or "sausage" shape at ends) |
| Equidistant from 2 points | Perpendicular bisector |
| Equidistant from 2 lines | Angle bisector |
Practice Problems
- Construct the perpendicular bisector of a 8 cm line.
- Construct the bisector of a 70° angle.
- Shade the region within 3 cm of point A and closer to B than C.
Want to check your answers and get step-by-step solutions?
Key Takeaways
Use compass and ruler — no measuring for bisectors.
Leave construction arcs visible (examiners check them).
Loci combine conditions — shade the intersection of regions.