Symmetry Class 6 Worksheet — Free PDF Download with Answers

Symmetry is one of the most visually appealing concepts in mathematics. A shape has symmetry if one part of it is a mirror image of another. When you fold a butterfly along its body, the two wings overlap perfectly — that fold line is the line of symmetry.

In Class 6, students study two types of symmetry: reflection symmetry (also called line symmetry or mirror symmetry) and an introduction to rotational symmetry. They learn to identify lines of symmetry in regular polygons, letters of the alphabet, and everyday objects. They also complete half-drawn figures using a given line of symmetry.

Symmetry is not just an abstract concept. Architects use it to design buildings, artists use it in patterns and rangoli, and scientists use it to classify crystals and molecules. Understanding symmetry sharpens observation skills and connects mathematics to art and nature.

* Line of symmetry (axis of symmetry) — A line that divides a figure into two identical halves that are mirror images of each other.
* Number of lines of symmetry:
- Equilateral triangle: $3$
- Square: $4$
- Rectangle: $2$
- Circle: infinite
- Regular pentagon: $5$
- Regular hexagon: $6$
- In general, a regular $n$-gon has $n$ lines of symmetry.
* Symmetric letters — Letters like $A, B, C, D, E, H, I, M, O, T, U, V, W, X, Y$ have at least one line of symmetry.
* Reflection symmetry — Each point on one side of the line has a corresponding point at the same perpendicular distance on the other side.
* Rotational symmetry — A figure has rotational symmetry if it looks the same after a rotation of less than $360^\circ$. The order of rotational symmetry is the number of times it coincides with itself during a full $360^\circ$ rotation.
- Square: order $4$ (coincides at $90^\circ, 180^\circ, 270^\circ, 360^\circ$).
- Equilateral triangle: order $3$.
* Completing a symmetric figure — Given half a figure and its line of symmetry, mirror each point across the line to draw the other half.

1. Print the PDF — Download from the links below. Keep graph paper, a ruler, and a small mirror handy.

2. Start with Level 1 (Easy) — 20 questions on identifying lines of symmetry, symmetric letters, and counting symmetry lines in basic shapes.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the included answer key.

5. Revise mistakes — For figure-completion errors, use a mirror to verify and redraw.

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

Level 1 — Easy

1. How many lines of symmetry does a square have?
Solution: $4$ (two diagonals and two lines through the midpoints of opposite sides).

2. Which of the following letters has a horizontal line of symmetry: $A, B, C, D$?
Solution: $B, C, D$ have horizontal lines of symmetry. $A$ has a vertical line of symmetry.

3. Draw the line(s) of symmetry for a rectangle.
Solution: $2$ lines — one horizontal through the midpoints of the longer sides, one vertical through the midpoints of the shorter sides.

Level 2 — Medium

1. Complete the following figure given that the dotted line is the line of symmetry. (A half-heart shape is shown.)
Solution: Mirror each point across the dotted line to complete the heart shape.

2. How many lines of symmetry does a regular hexagon have?
Solution: $6$ (three through opposite vertices, three through midpoints of opposite sides).

3. Does the letter $S$ have any line of symmetry?
Solution: No, $S$ does not have any line of symmetry. However, it has rotational symmetry of order $2$.

Level 3 — Hard

1. A figure has exactly $2$ lines of symmetry but no rotational symmetry of order $4$. What shape could it be?
Solution: A rectangle (not a square). It has $2$ lines of symmetry and rotational symmetry of order $2$, not $4$.

2. Find the order of rotational symmetry for a regular pentagon.
Solution: A regular pentagon coincides with itself at rotations of $72^\circ, 144^\circ, 216^\circ, 288^\circ,$ and $360^\circ$. Order $= 5$.

3. Design a rangoli pattern that has exactly $4$ lines of symmetry and rotational symmetry of order $4$.
Solution: A square-based pattern (e.g., a square with identical decorations in all four quadrants) satisfies both conditions.

CBSE (NCERT — Ganita Prakash / Math Magic)
The "Symmetry" chapter covers line symmetry with hands-on activities (paper folding, mirror placement). CBSE emphasises identifying and drawing lines of symmetry and completing symmetric figures. Rotational symmetry is introduced briefly.

ICSE (Selina / ML Aggarwal)
ICSE also covers symmetry with a similar scope but includes more diagram-based questions. ICSE exams test students on completing half-drawn figures on grid paper and counting lines of symmetry for complex shapes.

IB MYP (Mathematics Framework)
The IB embeds symmetry within the Geometry unit. Students explore symmetry in nature, art, and architecture through investigative tasks. The emphasis is on connecting symmetry to real-world contexts and communicating findings.

Key Differences:
* CBSE: Hands-on (paper folding, mirrors); focus on identification.
* ICSE: Grid-based figure completion; more diagram questions.
* IB: Real-world connections; investigation and communication.

Download your free Symmetry worksheets:

* Symmetry CBSE Worksheet — 60 questions aligned to NCERT
* Symmetry 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 — Upload a symmetry question and get a step-by-step solution.
* Spark Coach — AI tutor that guides with hints, not answers.
* Free Worksheets for All Classes — Browse worksheets from Class 1 to 10.
* Play Mode for Class 1-4 — Fun symmetry games for younger learners.

Explore more Class 6 worksheets:

* Lines and Angles Class 6 Worksheet
* Constructions & Practical Geometry Class 6 Worksheet
* Perimeter and Area Class 6 Worksheet
* Patterns in Mathematics Class 6 Worksheet
* Data Handling Class 6 Worksheet