What this chapter is about
This chapter teaches you how to draw shapes carefully using simple tools like a ruler (scale) and a compass. A compass is a tool with two arms — one has a sharp point, and the other holds a pencil. You use it to draw circles and arcs.
In earlier classes, you drew shapes by looking at them. Now you will learn to construct them with exact measurements. Construction means making a shape step by step using rules, not just sketching. You will learn to draw circles, copy line segments, make angles, and build triangles.
After this chapter, you will be able to use a compass and ruler to create shapes that are accurate. This skill helps in map-making, art, design, and even building houses!
Key ideas
- A compass draws circles and arcs by keeping one point fixed and moving the pencil arm around it.
- The radius is the distance from the centre of a circle to any point on the circle. All radii of the same circle are equal.
- A line segment is a straight line with two end points. You can copy a line segment using a ruler and compass.
- An arc is a part of a circle, like a curved piece cut from a bangle.
- To construct a triangle, you need three measurements — these could be the lengths of all three sides.
- Every construction has clear steps that must be followed in order.
- Marks and labels (like A, B, C) help you keep track of points during construction.
Formulas and facts to remember
- Radius: The distance from the centre to any point on a circle.
- Diameter: The distance across a circle through its centre. Diameter = 2 × radius.
- Arc: A part of the boundary of a circle.
- Line segment: A straight path between two fixed points.
- To copy a line segment: Open the compass to match the segment's length, then draw an arc from a new point.
- Triangle rule: A triangle has three sides. To construct it, you need to know the length of each side.
Worked examples
Example 1: Draw a circle with radius 3 cm.
Step 1: Mark a point on your paper and call it O. This is the centre.
Step 2: Open your compass so the distance between the point and the pencil tip is exactly 3 cm. Use a ruler to set this.
Step 3: Place the sharp point of the compass on O.
Step 4: Rotate the pencil arm all the way around, keeping the sharp point fixed.
You now have a circle with centre O and radius 3 cm.
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Example 2: Copy a line segment AB that is 5 cm long.
Step 1: Draw a line segment AB of length 5 cm using your ruler.
Step 2: Draw a new line below it. Mark a point P on this line.
Step 3: Open your compass and place the sharp point on A and the pencil on B.
Step 4: Without changing the compass opening, place the sharp point on P and draw an arc that cuts your line. Call this point Q.
PQ is now equal to AB — both are 5 cm.
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Example 3: Construct a triangle with sides 4 cm, 5 cm, and 6 cm.
Step 1: Draw a line segment of 6 cm using your ruler. Call the ends A and B.
Step 2: Open your compass to 4 cm. Place the sharp point on A and draw an arc above AB.
Step 3: Open your compass to 5 cm. Place the sharp point on B and draw an arc that crosses the first arc. Call this crossing point C.
Step 4: Use your ruler to join A to C and B to C.
Triangle ABC has sides 4 cm, 5 cm, and 6 cm.
Common mistakes
- Changing the compass opening while drawing an arc → Hold the compass firmly and do not press too hard.
- Not placing the compass point exactly on the marked point → Always check that the sharp point sits right on the dot.
- Drawing rough circles by moving the compass too fast → Rotate slowly and steadily for a neat circle.
- Forgetting to label points → Always write the letters (A, B, C) so you know which point is which.
- Measuring the radius but setting the compass to the diameter → Remember, radius is half the diameter.
Quick revision
- A compass and ruler let you construct shapes accurately.
- Radius is centre to edge; diameter is edge to edge through the centre.
- To copy a segment, match the compass opening to its length.
- For a triangle, draw one side first, then use arcs to find the third point.
- Label every point clearly during construction.
- Take your time — neat work beats fast work.