How do you construct a perpendicular bisector of a line segment?

1. Draw line segment AB. 2. With compass centred at A, draw arcs above and below AB (radius > half of AB). 3. With same radius centred at B, draw arcs that cut the previous arcs at points P and Q. 4. Draw line PQ — this is the perpendicular bisector. It passes through the midpoint of AB at 90°.

How do you bisect an angle?

1. Draw angle ABC. 2. With centre B and any radius, draw an arc cutting BA at P and BC at Q. 3. With centre P and centre Q (same radius), draw arcs inside the angle that intersect at R. 4. Draw ray BR — this bisects angle ABC, creating two equal angles.

How do you construct a 60° angle?

1. Draw a ray OA. 2. With centre O, draw an arc cutting OA at B. 3. With same radius centred at B, draw an arc cutting the first arc at C. 4. Draw ray OC — angle COA = 60°.

CBSE Class 6 Maths Chapter 14 Notes — Practical Geometry

Exercise Solutions Available

Step-by-step answers for all textbook questions in this chapter

View Solutions →

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.

Frequently Asked Questions

The basic geometry tools are: Ruler (scale) — for drawing and measuring line segments. Compass — for drawing circles and arcs, transferring lengths. Protractor — for measuring and drawing angles. Set squares (30-60-90 and 45-45-90) — for drawing specific angles and perpendicular lines. Divider — for comparing and transferring lengths.