Constructions & Practical Geometry Class 6 Worksheet — Free PDF Download with Answers

Geometric constructions are drawings made using only a compass and an unmarked straightedge (ruler). Unlike measurement-based drawing, constructions rely on pure geometric reasoning — you do not read off centimetre markings; instead, you use arcs and intersections to create exact shapes.

In Class 6, students learn to construct line segments of a given length, copy a line segment, construct perpendicular bisectors, bisect angles, and draw angles of $60^\circ$, $90^\circ$, $120^\circ$, and their halves. These skills are the foundation for more advanced constructions in Classes 7-9, such as constructing triangles and quadrilaterals.

Constructions develop precision, spatial reasoning, and logical thinking. When you construct the perpendicular bisector of a segment, you are physically proving that every point on that bisector is equidistant from the two endpoints — geometry comes alive through your hands.

* Line segment construction — Use a ruler to draw a segment of a given length, or use a compass to copy an existing segment.
* Circle — All points at a fixed distance (radius) from a centre. Drawn with a compass.
* Perpendicular bisector — A line perpendicular to a segment that passes through its midpoint. Constructed by drawing two arcs of equal radius from each endpoint.
* Angle bisector — A ray that divides an angle into two equal parts. Constructed using arcs from the vertex and their intersection.
* Standard angle constructions:
- $60^\circ$: Draw an arc from the vertex; from the arc's intersection, draw another arc of the same radius. The intersection gives $60^\circ$.
- $90^\circ$: Construct $60^\circ$, then bisect the remaining $30^\circ$ — or construct the perpendicular bisector of a segment.
- $120^\circ$: Two consecutive $60^\circ$ arcs.
- $45^\circ$: Bisect $90^\circ$.
- $30^\circ$: Bisect $60^\circ$.
* Perpendicular from/to a point — Drop a perpendicular from a point to a line using arcs.
* Equilateral triangle — All sides equal; each angle $= 60^\circ$. Constructed using the $60^\circ$ method.

1. Print the PDF — Download from the links below. Keep compass, ruler, protractor, and sharp pencil ready.

2. Start with Level 1 (Easy) — 20 questions on drawing segments, circles, and basic angle constructions.

3. Time yourself — 20 minutes for Level 1, 25 for Level 2, 30 for Level 3 (constructions take more time than computation).

4. Check answers — Use the answer key for verification. For constructions, check measurements with a protractor/ruler.

5. Revise mistakes — Redo incorrect constructions on a fresh sheet, tracing each step carefully.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Draw a line segment $\overline{AB} = 6.5$ cm.
Solution: Use a ruler to mark point $A$, then measure $6.5$ cm and mark point $B$. Draw a straight line joining $A$ and $B$.

2. Draw a circle of radius $3$ cm.
Solution: Set the compass to $3$ cm. Place the needle on the centre point and draw a full arc.

3. Construct an angle of $60^\circ$ at point $O$.
Solution: Draw ray $\overrightarrow{OA}$. With $O$ as centre, draw an arc cutting $\overrightarrow{OA}$ at $P$. With $P$ as centre and same radius, draw an arc cutting the first arc at $Q$. Draw $\overrightarrow{OQ}$. $\angle AOQ = 60^\circ$.

Level 2 — Medium

1. Construct the perpendicular bisector of $\overline{PQ} = 8$ cm.
Solution: With $P$ as centre and radius $> 4$ cm, draw arcs above and below $\overline{PQ}$. Repeat with $Q$ as centre and same radius. Join the two intersection points. This line is the perpendicular bisector.

2. Construct an angle of $30^\circ$.
Solution: Construct $60^\circ$ first, then bisect it to get $30^\circ$.

3. Construct an angle of $90^\circ$ using a compass.
Solution: Construct $60^\circ$ at a point on a ray. From the $60^\circ$ arc point, construct another $60^\circ$ to get $120^\circ$. Bisect the angle between $60^\circ$ and $120^\circ$ to get $90^\circ$.

Level 3 — Hard

1. Construct an equilateral triangle with side $5$ cm.
Solution: Draw $\overline{AB} = 5$ cm. With $A$ as centre and radius $5$ cm, draw an arc. With $B$ as centre and same radius, draw an arc. Label intersection $C$. Join $AC$ and $BC$.

2. Draw a line segment $\overline{AB} = 7$ cm. Construct a perpendicular from the midpoint of $\overline{AB}$, and mark a point $C$ on it at $4$ cm from $\overline{AB}$. What kind of triangle is $\triangle ABC$?
Solution: $\triangle ABC$ is isosceles because $C$ lies on the perpendicular bisector, so $CA = CB$.

3. Construct an angle of $75^\circ$.
Solution: Construct $90^\circ$ and $60^\circ$ at the same point. Bisect the $30^\circ$ difference to get $15^\circ$. Add $15^\circ$ to $60^\circ$ to get $75^\circ$.

CBSE (NCERT — Ganita Prakash)
The chapter "Playing with Constructions" introduces compass and ruler constructions through exploratory activities. CBSE emphasises the process (steps of construction) rather than just the final figure. Students are asked to describe construction steps in words.

ICSE (Selina / ML Aggarwal)
ICSE covers this under "Practical Geometry" with a focus on precision. ICSE exams include construction questions that require students to draw accurately and measure the result. There is more emphasis on constructing triangles given certain conditions (SSS, SAS).

IB MYP (Mathematics Framework)
The IB does not have a dedicated constructions chapter at the MYP 1 level, but construction activities appear as enrichment within the Geometry unit. IB students benefit from this worksheet as it develops spatial reasoning skills valued in the MYP assessment criteria.

Key Differences:
* CBSE: Exploratory; emphasis on process description.
* ICSE: Precision-oriented; triangle constructions included.
* IB: Enrichment activity; embedded within geometry investigations.

Download your free Constructions worksheets:

* Playing with Constructions CBSE Worksheet — 60 questions aligned to NCERT
* Practical Geometry ICSE Worksheet — 60 questions aligned to Selina / ML Aggarwal

Practise online:

* Practice Online — CBSE
* Practice Online — ICSE

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Need help with a construction step? Get a step-by-step solution.
* Spark Coach — AI tutor that guides your thinking with hints.
* Free Worksheets for All Classes — Worksheets from Class 1 to 10 across all boards.
* Play Mode for Class 1-4 — Fun geometry games for younger learners.

Explore more Class 6 geometry worksheets:

* Lines and Angles Class 6 Worksheet
* Symmetry Class 6 Worksheet
* Perimeter and Area Class 6 Worksheet
* Patterns in Mathematics Class 6 Worksheet
* Ganita Prakash Class 6 Worksheet