Symmetry Class 7 Worksheet — Free PDF Download with Answers

Symmetry is one of those chapters where everyone assumes it is easy. Then the exam arrives and students realise they cannot remember whether a rectangle has two lines of symmetry or four. Or how many lines of symmetry a regular hexagon has. The only reliable fix is to draw these shapes by hand, over and over, until the pictures are burnt into memory.

One school I visit uses a simple worksheet routine for symmetry. Every Monday morning, students are given a page with ten shapes and asked to draw all lines of symmetry. By Friday, the routine is complete with rotational symmetry. By the end of the month, every student in Class 7 can answer any symmetry question without thinking. That is the power of focused paper practice.

Worksheets also teach you to fold and imagine. A symmetry line is, in essence, a line where you could fold the shape and have both halves match. Holding a printed page and mentally folding it along different lines is the best way to develop this sense. An app cannot give you the same tactile feedback.

Another strength of paper practice is that you can draw your own shapes. After ten solved examples, a good habit is to draw a shape of your own and test it. That creative element is almost entirely missing from app based learning.

Finally, worksheets are quiet. Symmetry needs observation, not typing. A clean worksheet session with no distractions lets students actually look at the shapes.

The worksheet covers every sub topic from the Class 7 Symmetry chapter.

Sub topics:

* Lines of symmetry for regular polygons
* Lines of symmetry for irregular shapes
* Reflection symmetry
* Rotational symmetry
* Centre of rotation
* Order of rotational symmetry
* Angle of rotation
* Combined reflection and rotational symmetry

Level breakdown:

Total 60 questions with a full answer key.

Revise these points first.

* Line of symmetry — A line that divides a figure into two mirror images.
* Reflection symmetry — A figure has reflection symmetry if it has at least one line of symmetry.
* Regular polygon symmetry — A regular polygon with $n$ sides has exactly $n$ lines of symmetry.
* Rotational symmetry — A figure has rotational symmetry if it looks the same after being rotated by some angle less than $360\degree$.
* Order of rotational symmetry — The number of times the figure looks the same during one full rotation.
* Angle of rotation — $\dfrac{360\degree}{\text{order}}$.
* Key examples
* Equilateral triangle: $3$ lines of symmetry, order $3$ rotation.
* Square: $4$ lines of symmetry, order $4$ rotation.
* Regular hexagon: $6$ lines of symmetry, order $6$ rotation.
* Circle: infinite lines of symmetry, infinite order rotation.

Quick tip: For any regular polygon, the number of lines of symmetry equals the number of sides and also equals the order of rotational symmetry.

Level 1 — Easy

1. How many lines of symmetry does a rectangle have?
Solution: $2$ — one horizontal and one vertical through the centre.

2. Does an equilateral triangle have rotational symmetry? If so, state the order.
Solution: Yes, order $3$.

3. Does the letter H have a line of symmetry?
Solution: Yes, both horizontal and vertical lines of symmetry.

Level 2 — Medium

1. A shape has rotational symmetry of order $4$. What is the angle of rotation?
Solution: $\dfrac{360}{4} = 90\degree$.

2. How many lines of symmetry does a regular pentagon have?
Solution: $5$.

3. Name a shape with reflection symmetry but no rotational symmetry.
Solution: An isoceles trapezium or the letter $T$.

Level 3 — Hard

1. A regular polygon has $8$ sides. State the number of lines of symmetry, order of rotational symmetry and the angle of rotation.
Solution: $8$ lines of symmetry, order $8$, angle $\dfrac{360}{8} = 45\degree$.

2. Which shape has both order $2$ rotational symmetry and exactly $2$ lines of symmetry?
Solution: A rectangle or a rhombus.

3. The letter $S$ has rotational symmetry of order $2$ but no line of symmetry. Name another letter with the same property.
Solution: $Z$ or $N$.

1. Print — Use plain A4 paper and a pencil.
2. Warm up — Draw three shapes and mark their lines of symmetry.
3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.
4. Check answers — Use the answer key.
5. Revise mistakes — Redraw the shape and find the symmetry correctly.
6. Try again — Redo wrong questions next day.

Daily plan: 20 minutes per day for two weeks.

Weekly revision: Each Sunday, draw five shapes from memory and list their lines of symmetry and order of rotational symmetry.

1. Confusing diagonals with lines of symmetry — A rectangle has diagonals, but its diagonals are not lines of symmetry. Only the horizontal and vertical lines through the centre are.

2. Missing rotational symmetry — Students sometimes assume a shape has no rotational symmetry when it actually does.

3. Wrong order count — Forgetting that the full $360\degree$ rotation counts as one position. A square returns to the same position $4$ times in one rotation, so order $4$.

4. Scalene triangles — Students sometimes assume a scalene triangle has a line of symmetry. It does not.

5. Regular vs irregular confusion — Assuming an irregular hexagon has $6$ lines of symmetry because a hexagon has $6$ sides. Only regular polygons have this property.

6. Reflection confusion — Drawing the line of symmetry but forgetting to check that the two halves actually match.

CBSE (NCERT)
Symmetry is Chapter 12 of NCERT Class 7 maths. Weightage is around 8 marks. Questions test both reflection and rotational symmetry with a focus on recognising common shapes.

ICSE (Selina / ML Aggarwal)
ICSE treats symmetry with more formal definitions and includes questions on mapping a figure onto itself under rotation. Weightage is around 10 marks.

IB MYP
IB MYP handles symmetry through transformations. Students learn reflections, rotations and translations as separate operations and then investigate which shapes are preserved under each.

Download the free Class 7 Symmetry worksheet:

* Congruence and Symmetry CBSE Worksheet
* Symmetry ICSE Worksheet

Online practice:

* Symmetry Online — CBSE
* Symmetry Online — ICSE

* AI Maths Solver — Upload any symmetry question for a step by step solution.
* Spark Coach — AI tutor with hints.
* Class 7 Maths Complete Guide
* All Worksheets Hub
* Class 7 Formulas

Week 1: Lines of symmetry

* Day 1: Read the chapter and draw common regular shapes with their lines of symmetry.
* Day 2: Level 1 questions 1 to 10.
* Day 3: Level 1 questions 11 to 20.
* Day 4: Level 2 lines of symmetry questions.
* Day 5: Level 2 rotational symmetry questions.
* Day 6: Redo wrong answers.
* Day 7: Rest.

Week 2: Rotation and combined symmetry

* Day 8: Level 3 questions 1 to 10.
* Day 9: Level 3 questions 11 to 20.
* Day 10: Redo wrong answers.
* Day 11: Draw five of your own shapes and analyse their symmetry.
* Day 12: Mixed quiz.
* Day 13: Mock test (30 minutes).
* Day 14: Review.

* Class 7 Congruence Worksheet
* Class 7 Triangles Worksheet
* Class 7 Lines and Angles Worksheet
* Class 7 Visualising Solid Shapes Worksheet
* Class 7 Maths Complete Guide