Constructions and loci · Grade 9
In Grade 9 you learn: perpendicular bisectors and angle bisectors; constructions with compasses.
Constructions are accurate drawings made with a ruler and compasses only. A locus (plural loci) is the set of all points that follow a rule, such as “3 m from a post” or “the same distance from two points”, and is drawn with the same constructions.
Key facts
- Perpendicular bisector of AB: equal arcs from A and B; join the crossings. Its points are equidistant from A and B.
- Angle bisector: an arc from the corner cuts both arms; equal arcs from those points cross on the bisector.
- Triangle from three sides: draw one side, then arcs of the other two lengths from its ends.
- A fixed distance from a line makes parallel lines (with semicircles round the ends of a line segment).
- Leave construction arcs showing: they are your working.
Worked examples
Example 1
Use a ruler and compasses to construct the perpendicular bisector of the line AB.
Answer: Equal arcs from A and from B cross at two points; the line through them cuts AB in half at right angles.
Example 2
The angle AOB is 52°. Use compasses to bisect it (cut it into two equal angles).
Answer: Two angles of 26°, either side of the bisector OR.
Example 3
Construct triangle ABC with AB = 6 cm, AC = 5 cm and BC = 4 cm.
Answer: C is where an arc of radius 5 cm from A crosses an arc of radius 4 cm from B.