Symmetry Class 6 ICSE Worksheet Free PDF Download with Answers

Class 6 Maths Worksheet — Free PDF with Answers

This is your one-stop class 6 maths worksheet collection — every topic, every chapter, completely free with step-by-step answers. SparkEd's Class 6 maths practice covers the full ICSE syllabus with 60 questions per topic, and each worksheet comes as a printable PDF.

Every worksheet is aligned to the latest ICSE/CISCE syllabus pattern.

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Symmetry — Mathematics in Nature, Art, and Design

Symmetry is everywhere — in butterfly wings, snowflakes, building facades, and rangoli patterns. The ICSE Class 6 syllabus introduces symmetry as a geometric concept, teaching you to identify and count lines of symmetry and understand rotational symmetry.

A figure has a line of symmetry if folding it along that line makes both halves match exactly. A figure has rotational symmetry if rotating it by less than $360\degree$ about its centre produces the same figure.

This worksheet builds from identifying symmetry in everyday objects to working with symmetric figures on a coordinate grid.

What Does This Worksheet Cover?

Aligned with the ICSE Class 6 Symmetry chapter:

- Lines of symmetry — identifying and drawing for given shapes
- Counting lines of symmetry — regular polygons, letters, everyday objects
- Reflection symmetry — completing a figure given half and a mirror line
- Rotational symmetry — order of rotational symmetry
- Centre of rotation — identifying the point of rotation
- Symmetry in regular polygons — a regular $n$-gon has $n$ lines of symmetry
- Creating symmetric patterns — on dot grids and squared paper

| Level | Focus | Count |
|-------|-------|-------|
| Level 1 | Identify lines of symmetry, count for basic shapes and letters | 20 |
| Level 2 | Complete symmetric figures, reflection on grid, rotational symmetry order | 20 |
| Level 3 | Multi-step symmetry reasoning, patterns, combining line and rotational symmetry | 20 |

Sample Questions

Level 1 — Warm Up

1. How many lines of symmetry does (a) a square (b) an equilateral triangle (c) a circle have?
2. Which capital letters of the English alphabet have exactly one vertical line of symmetry?
3. Draw all lines of symmetry for a regular hexagon.

Level 2 — Build Confidence

1. Half of a symmetric figure is drawn on a grid. Complete the other half using the given line of symmetry.
2. What is the order of rotational symmetry of (a) a square (b) an equilateral triangle (c) a regular pentagon?
3. A shape has $4$ lines of symmetry and rotational symmetry of order $4$. Name the shape.

Level 3 — Push Yourself

1. A figure has rotational symmetry of order $3$ but no lines of symmetry. Draw an example of such a figure.
2. How many lines of symmetry does a regular $12$-gon (dodecagon) have? What is its order of rotational symmetry?
3. On a grid, create a pattern that has exactly $2$ lines of symmetry (one horizontal, one vertical) and rotational symmetry of order $2$.

Tips for ICSE Symmetry Questions

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Related Worksheets

Explore more geometry:

- Basic Geometry Class 6 ICSE Worksheet — shapes and angles form the basis of symmetry
- Practical Geometry Class 6 ICSE Worksheet — construct symmetric figures with compass
- Area & Perimeter Class 6 ICSE Worksheet — symmetric shapes have measurement shortcuts

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