Playing with Constructions | Mathematics Grade 6 CBSE

Play with it

The six ideas of construction

Constructions use just two tools, but they build everything from a line segment to a square. Tap each term to see what it is and how it is drawn.

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The three big ideas

A ruler draws straight lines and measures lengths; a compass draws arcs and circles and carries an exact length from one place to another.
A line segment is a straight path with two end points — say A and B — so it has a fixed length we can write as AB.
To draw a 5 cm segment: mark a point A, lay the ruler along it, and mark B at the 5 cm line. Join A to B.
To copy a segment without re-measuring, open the compass so its two points sit exactly on A and B, then place one point on a new spot and mark the same width — the new segment is identical.

Worked example. You have a segment AB and want a new segment PQ exactly as long, but your ruler markings are worn out. How do you do it?

Open the compass so one point rests on A and the pencil point on B — this captures the length AB.

Without changing the opening, put the compass point on P and swing a small arc to mark Q. Join P to Q: now PQ = AB exactly.

Common mistake: letting the compass slip and change its opening between A and the new point. Hold it steady — even a tiny change spoils the copied length.

A circle is the set of all points that are the same distance from a fixed point called the centre.
That fixed distance is the radius. A straight line through the centre, from one side of the circle to the other, is the diameter, and diameter = 2 × radius.
To draw a circle of radius 3 cm: open the compass to 3 cm using a ruler, press the metal point firmly on the centre, and turn the pencil all the way round.
Because the compass opening never changes as it turns, every point traced stays exactly 3 cm from the centre — that is why the shape is a perfect circle.

Worked example. A circle has a radius of 3.5 cm. What is its diameter, and how would you mark a point that lies on the circle?

Diameter = 2 × radius = 2 × 3.5 = 7 cm.

Any point you reach by opening the compass to 3.5 cm from the centre lies on the circle — swing the arc and the pencil mark is on it.

Common mistake: opening the compass to the diameter instead of the radius. The compass width is the radius — set it to half the diameter.

Two lines are perpendicular when they cross at a right angle (90°). A set square or the right-angle corner of the ruler helps mark one quickly.
Right angles are the building blocks of squares and rectangles: a square has four equal sides and four right angles; a rectangle has equal opposite sides and four right angles.
To build a square of side 5 cm: draw a 5 cm base, raise perpendiculars (90°) at both ends, mark 5 cm up each, and join the top — every side 5 cm, every angle 90°.
Always check the figure afterwards: are the sides the right length, and are the corners true right angles?

Worked example. Construct a rectangle 6 cm long and 4 cm wide. List the steps.

1. Draw base AB = 6 cm with the ruler.

2. At A and at B, construct perpendiculars (right angles) to AB.

3. Along each perpendicular, mark a point 4 cm up — call them D (above A) and C (above B).

4. Join D to C. ABCD is the required rectangle: opposite sides 6 cm and 4 cm, all angles 90°.

Common mistake: drawing the top side slanted. If the perpendiculars are not truly 90°, the figure becomes a leaning parallelogram instead of a rectangle.

Where you'll meet it

Constructions at work

Carpentry & building

A carpenter marks right angles before cutting a wooden frame; a mason checks that walls meet at 90°. Perpendiculars keep furniture and buildings square and stable.

Rangoli & design

Many rangoli and kolam patterns start from a compass circle and equally spaced dots. The same radius, swung around, places petals and points in perfect balance.

Maps & plans

To mark every spot within 2 km of a well on a village map, you draw a circle of that radius. The compass turns "the same distance all around" into an exact boundary.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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