Playing with Constructions
Geometry is not only about looking at shapes but about making them accurately. This Class 6 Ganita Prakash chapter introduces the ruler and compass and shows how to draw line segments of a given length, draw circles, and combine these steps to construct neat figures.
Learning objectives
- Use a ruler and compass correctly.
- Draw a line segment of a given length.
- Draw a circle of a given radius.
- Construct simple figures step by step.
Key concepts
Tools of construction
Accurate drawings use a ruler to draw and measure straight lengths and a compass to draw circles and mark off equal lengths. A sharp pencil keeps lines thin and precise. In true construction we rely on the ruler only for straight edges and lengths, and the compass for curves and copying distances.
Drawing a line segment
To draw a line segment of, say, 5 cm, place the ruler's zero mark at the starting point, mark the point at 5 cm, and join the two with a straight line. A compass can then copy this length elsewhere by opening it to the segment and marking the same distance.
Drawing a circle
A circle is the set of points the same distance from a fixed centre. To draw one, open the compass to the required radius, place its sharp point at the centre, and turn it to sweep out the circle. The opening of the compass stays fixed as the radius throughout.
Building figures step by step
Larger figures are built by combining basic steps — drawing segments of given lengths, marking equal distances with the compass, and joining points. Following the steps carefully and in order produces a clean, accurate figure such as a triangle or a square.
Key definitions
- Ruler
- A straight-edged tool for drawing and measuring straight lengths.
- Compass
- A tool for drawing circles and copying equal lengths.
- Radius
- The fixed distance from the centre of a circle to any point on it.
- Construction
- An accurate drawing made with geometric tools.
Solved examples
Q1. Which tool would you use to draw a circle?
Solution: A compass, opened to the required radius.
Q2. How do you copy a 4 cm segment without measuring again?
Solution: Open the compass to the 4 cm segment, then mark the same opening elsewhere.
Q3. While drawing a circle, what must stay the same?
Solution: The compass opening (the radius) must not change.
Common mistakes to avoid
- Letting the compass opening slip while drawing a circle.
- Starting a segment from the ruler's edge instead of the zero mark.
- Using a blunt pencil, giving thick, inaccurate lines.
- Skipping construction steps or doing them out of order.
Playing with Constructions — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
Which tool is used to draw a circle?
Practice questions
Short answer
What is a compass used for?
To draw circles and to copy or mark off equal lengths.
What does the compass opening represent when drawing a circle?
The radius of the circle.
Why should the pencil be sharp during construction?
To draw thin, precise lines for an accurate figure.
Long answer
Describe the steps to draw a circle of radius 3 cm using a compass.
First, open the compass and set its opening to 3 cm by placing the sharp point at the ruler's zero mark and the pencil tip at the 3 cm mark. Next, place the sharp point firmly on the chosen centre point on the paper. Then, holding the opening steady, turn the compass all the way around so the pencil sweeps a smooth curve. The result is a circle of radius 3 cm; keeping the opening fixed throughout is what makes every point the same distance from the centre.
Why is the compass essential for accurate constructions, more than measuring by eye?
The compass can hold a fixed distance and reproduce it exactly anywhere on the paper, which lets us copy lengths and draw circles precisely without re-measuring. Measuring by eye, or re-reading a ruler each time, introduces small errors that build up and spoil a figure. By transferring the same opening from one place to another, the compass guarantees equal lengths and true curves, which is why constructions rely on it together with the straight edge of the ruler.
HOTS (Higher Order Thinking)
How could you use a compass to mark three points exactly 4 cm from a single point?
Open the compass to 4 cm, place its point at the centre, and mark arcs at three places; every marked point is then exactly 4 cm away.
Two circles are drawn with the same compass opening but different centres. What is the same about them?
They have equal radii, so the two circles are exactly the same size.
Quick revision
Revision notes
- Ruler: straight lines and lengths; compass: circles and equal lengths.
- Start a segment from the ruler's zero mark.
- Circle = points at a fixed distance (radius) from a centre.
- Keep the compass opening fixed while drawing a circle.
Key takeaways
- Constructions are about accuracy, not rough sketches.
- The compass holds and copies a fixed distance.
- Careful, ordered steps give clean figures.
Frequently asked questions
What is the difference between a ruler and a compass?
A ruler draws and measures straight lengths; a compass draws circles and copies equal lengths.
What is the radius of a circle?
The fixed distance from the centre to any point on the circle.
Why use a compass instead of measuring each time?
It reproduces a fixed length exactly, avoiding repeated measuring errors.