Playing with Constructions — Class 6 Maths (Ganita Prakash)
1. About This Chapter
Playing with Constructions is the hands-on geometry chapter of Ganita Prakash. Armed with just a compass and a ruler (an unmarked straightedge), students learn to create precise geometric figures. This chapter connects the theoretical knowledge from Lines and Angles (Chapter 2) with practical drawing skills.
2. Tools of Construction
The Ruler (Straightedge)
- Used to draw straight lines
- In constructions, it is unmarked — no measurements are taken from it
- Used to connect points
The Compass
- Used to draw circles and arcs
- Used to mark equal distances
- Used to copy lengths from one place to another
3. Drawing a Circle
To draw a circle with a compass:
- Mark the centre point O
- Set the compass to the desired radius
- Place the pointed end on O
- Rotate the pencil end smoothly to draw the circle
Key terms:
- Centre: The fixed point (O)
- Radius: Distance from centre to any point on the circle
- Diameter: A line through the centre touching the circle at two points (diameter = 2 × radius)
- Chord: Any line segment joining two points on the circle
4. Constructing a Line Segment of Given Length
To construct a line segment of a given length (say 5 cm):
- Draw a ray (a starting point A with a line going right)
- Set compass to 5 cm using a ruler
- Place compass point on A, draw an arc intersecting the ray
- Label the intersection as B
- AB is the required line segment of 5 cm
5. Constructing the Perpendicular Bisector
The perpendicular bisector of a line segment is a line that:
- Passes through the midpoint of the segment
- Is perpendicular (at 90°) to the segment
Construction Steps:
- Draw line segment AB
- With A as centre, radius MORE than half of AB, draw an arc above and below AB
- With B as centre, SAME radius, draw arcs above and below AB
- The arcs intersect at points P (above) and Q (below)
- Join P and Q — this is the perpendicular bisector
Property: Any point on the perpendicular bisector is equidistant from A and B.
6. Constructing an Angle Bisector
The angle bisector divides an angle into two equal parts.
Construction Steps:
- Draw angle ∠ABC with vertex B
- With B as centre, any convenient radius, draw an arc cutting BA at P and BC at Q
- With P as centre, draw an arc inside the angle
- With Q as centre, SAME radius, draw another arc intersecting the first at R
- Join B to R — BR is the angle bisector
Property: Every point on the angle bisector is equidistant from the two arms of the angle.
7. Constructing Angles: 60° and 120°
60° Angle:
- Draw a ray AB
- With A as centre, any radius, draw an arc cutting AB at P
- With P as centre, SAME radius, draw an arc intersecting the first arc at Q
- Join A to Q — ∠BAQ = 60°
This works because an equilateral triangle has all angles = 60°.
120° Angle:
Construct 60°, then from Q (instead of P), repeat the same arc to get R. ∠BAR = 120°.
8. Constructing a 90° Angle
- Draw a ray AB
- Construct 60° at A (get point Q)
- Construct 120° at A (get point R)
- Bisect the angle between 60° and 120° — this gives 90°
Alternatively, construct the perpendicular bisector method at point A.
9. Copying an Angle
To copy a given angle ∠XYZ to a new location:
- Draw a ray AB (this will be one arm of the new angle)
- With Y as centre, draw an arc cutting YX at P and YZ at Q
- With A as centre, SAME radius, draw an arc cutting AB at C
- Measure distance PQ with compass
- With C as centre, radius = PQ, draw an arc intersecting the first arc from A at D
- Join A to D — ∠BAD equals ∠XYZ
10. Key Concepts Summary
| Construction | Key Tool | Difficulty |
|---|---|---|
| Circle | Compass | Easy |
| Line segment of given length | Compass + Ruler | Easy |
| Perpendicular Bisector | Compass + Ruler | Medium |
| Angle Bisector | Compass + Ruler | Medium |
| 60° Angle | Compass + Ruler | Medium |
| 120° Angle | Compass + Ruler | Medium |
| 90° Angle | Compass + Ruler | Hard |
| Copy an Angle | Compass + Ruler | Hard |
11. Important Vocabulary
- Compass: A drawing instrument with two legs — one pointed, one with a pencil
- Ruler/Straightedge: An unmarked tool for drawing straight lines
- Radius: Distance from centre to any point on a circle
- Arc: A part of the circumference of a circle
- Bisect: To divide into two equal parts
- Perpendicular: At right angles (90°)
12. Worked Examples
Example 1: Draw AB = 6.5 cm, then its perpendicular bisector.
Steps: Use compass set to >3.25 cm. Draw arcs from A and B. Connect the intersections.
Example 2: Construct ∠POR = 90° and bisect it to get 45°.
Steps: Construct 60° + 30° or use 60°/120° bisection. Then bisect the 90°.
Example 3: Construct a circle of radius 4 cm and mark its centre, a radius, and a diameter.
- Centre: O
- Radius: OA = 4 cm
- Diameter: AB = 8 cm passing through O
13. Conclusion
Playing with Constructions transforms geometry from abstract theory to hands-on practice. The precision of compass-and-ruler constructions teaches patience, accuracy, and spatial reasoning. These constructions form the foundation for all geometric proofs and constructions in higher classes — from triangles (Class 7-9) to tangents (Class 10).
