Geometry Construction Tools
| Tool | Use |
|---|---|
| Ruler (scale) | Drawing line segments; measuring length |
| Compass | Drawing circles and arcs; copying lengths |
| Protractor | Measuring and drawing angles |
| Set square | Drawing perpendicular lines; specific angles (30°, 45°, 60°, 90°) |
| Divider | Comparing and transferring lengths |
Drawing a Circle
Using a compass:
1. Mark the centre point O. 2. Set the compass to the required radius. 3. Keep the needle at O; rotate the compass to draw the full circle.
Example: Draw a circle of radius 3.5 cm.
- Set compass to 3.5 cm using the ruler.
- Place needle at O, sweep around to complete the circle.
Constructing a Line Segment of Given Length
To draw a line segment of length 5.4 cm:
1. Draw a ray from point A. 2. Use divider/ruler to mark 5.4 cm from A — label that point B. 3. AB is the required line segment.
Drawing a Copy of a Given Line Segment
Using compass and ruler (without measuring directly):
1. Draw a ray from point P. 2. Measure the given segment AB with a compass. 3. Place compass needle at P; mark off the same length → Q. 4. PQ = AB.
Perpendicular Lines
Perpendicular to a point on a line (using protractor):
1. Mark point P on line l. 2. Use protractor to mark 90°. 3. Draw the perpendicular.
Perpendicular Bisector of a Line Segment
A perpendicular bisector passes through the midpoint of a segment and is perpendicular (90°) to it.
Construction steps:
1. Draw line segment AB. 2. Open compass to a radius greater than half of AB. 3. With centre A, draw arcs above and below AB. 4. With same radius and centre B, draw arcs cutting the previous arcs at P and Q. 5. Join P and Q — this is the perpendicular bisector.
PQ passes through the midpoint M of AB, and PM ⊥ AB.
Constructing an Angle of a Given Measure
Using a protractor:
1. Draw a ray OA. 2. Place the protractor's centre on O, base line on OA. 3. Mark the point corresponding to the required angle (e.g., 75°) — label it B. 4. Remove protractor; draw ray OB. 5. ∠BOA = 75°.
Angle Bisector
A ray that divides an angle into two equal halves.
Construction steps:
1. Draw angle ∠ABC. 2. With centre B, draw an arc of any radius cutting BA at P and BC at Q. 3. With centre P and same radius, draw an arc inside the angle. 4. With centre Q and same radius, draw an arc to intersect the previous arc at R. 5. Draw ray BR — this bisects ∠ABC.
∠ABR = ∠RBC = ½ × ∠ABC
Constructing Special Angles (Using Compass)
60° Angle
1. Draw ray OA. 2. Draw an arc from O cutting OA at B (any radius r). 3. With centre B, same radius, draw an arc cutting the first arc at C. 4. Draw ray OC → ∠COA = 60°.
120° Angle
After constructing 60° at C, continue the arc:
- With centre C, same radius, mark D.
- ∠DOA = 120°.
30° Angle
Bisect a 60° angle → 30°
90° Angle
1. Draw ray OA. 2. Construct 60° → OC. 3. Bisect the remaining 120° angle? — Actually:
- Construct 60°, then from C, construct another 60° → you get 120°.
- Bisect the 120° angle → 60°. Not quite.
- Simpler: use the perpendicular bisector concept — the right bisector of any segment gives a 90° angle.
45° Angle: Bisect a 90° angle.
Key Vocabulary
| Term | Meaning |
|---|---|
| Compass | Tool for drawing circles and arcs |
| Divider | Tool for comparing and copying lengths |
| Protractor | Tool for measuring angles |
| Perpendicular bisector | Line perpendicular to a segment at its midpoint |
| Angle bisector | Ray dividing an angle into two equal parts |
| Arc | Part of a circle |
| Radius | Distance from centre to circle |
Exam Tips
- Always write all construction steps — marks are given for procedure, not just the final figure.
- Perpendicular bisector: both arcs must have the same radius; radius must be more than half the segment length.
- Angle bisector: both arcs from P and Q must use the same radius.
- Use a sharp pencil — accuracy matters in construction questions.
- 60°: constructed using a compass (equilateral triangle property). This is the foundation for 30°, 120°, etc.
- Construction questions in exams are 3–5 marks — practice each construction multiple times.