Playing with Constructions Sums for Class 6 — Free CBSE Worksheet PDF with Answers

Playing with Constructions is unique because you actually create geometry with your hands. With just a compass and a straight edge, you can draw perfect circles, copy line segments, construct angles, bisect both segments and angles, and make beautiful inscribed shapes. The new NCERT Ganita Prakash textbook (Chapter 8) for Class 6 CBSE makes constructions feel like art — you finish the chapter with rosettes and Rangoli-like designs.

Construction is precision work. A sharp pencil, a tightly screwed compass, and clean technique are essential. Examiners look at the construction arcs you leave on the page — these prove you used the correct method, not measurement. Never erase your construction arcs.

This worksheet has 60 questions split across three levels. Level 1 covers circles, copying segments, and constructing basic angles ($60°$). Level 2 builds up to perpendicular bisectors, angle bisectors, and inscribed shapes. Level 3 covers complex multi-step constructions, rosette designs, and reasoning about why constructions work.

To draw a circle, set your compass to the desired radius (say, $4$ cm), place the metal point firmly at the centre, and rotate the pencil arm in one smooth motion. Mark the centre as $O$. Any line from $O$ to a point on the circle is a radius and equals $4$ cm.

To copy a line segment $AB$ of length $6.5$ cm: open your compass to span $A$ and $B$ exactly. Mark a fresh point $C$, place the compass point at $C$, and draw a small arc. The pencil mark on the arc is point $D$ such that $CD = AB$. Then join $C$ and $D$. This 'compass equals length' technique is used everywhere in constructions.

To construct a $60°$ angle: draw a ray from a point $A$. Place the compass at $A$ and draw an arc cutting the ray at point $P$. Without changing the compass width, place the compass at $P$ and draw another arc that intersects the first arc at point $Q$. Join $A$ to $Q$. The angle $\angle PAQ = 60°$. This works because triangle $APQ$ is equilateral by construction.

To construct the perpendicular bisector of segment $PQ$ of length $8$ cm: open the compass to more than half $PQ$ (say, $5$ cm). Place the point at $P$ and draw arcs above and below $PQ$. Without changing the compass, place the point at $Q$ and draw arcs that intersect the first ones. Join the two intersection points. This line is the perpendicular bisector — it crosses $PQ$ at its midpoint $M$ at exactly $90°$. Every point on this bisector is equidistant from $P$ and $Q$.

An equilateral triangle inscribed in a circle of radius $r$: draw the circle and a vertex at any point on it. Without changing the compass radius (still $r$), step around the circle marking arcs — they land exactly $r$ apart, dividing the circle into 6 equal arcs. Connect every second mark to make an equilateral triangle. Connect all 6 marks to make a regular hexagon.

A 6-petal rosette uses the same idea. After marking 6 equally spaced points on a circle, place the compass at each point in turn (still with radius $r$) and draw an arc inside the circle. The arcs create the classic 6-petal flower pattern seen on temple walls and in geometry textbooks. The mathematical reason this works is that the chord length equal to the radius subtends $60°$ at the centre, so 6 such chords go all the way around.