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📗 Class 7 maths · session 12 of 12 · 60 minutes · 🎁 free with an account

Symmetry and solid shapes

Welcome aboard, superhero cadet! Captain Calc needs your help to inspect superhero logos and 3D space bases for perfect symmetry.

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🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.

A complete lesson · 60 minutes

Teach it, see it, practise it, all on this page.

Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.

🎁 Unlock free with an accountRead part 1 free
  1. Warm-up3 min
  2. Warm-up games5 min
  3. Line Symmetry in 2D Shapes8 min
  4. Rotational Symmetry7 min
  5. 3D Solid Shapes and Their Components7 min
  6. Euler's Formula for Polyhedrons7 min
  7. Symmetry Scanner Mission6 min
  8. 3D Base Builder5 min
  9. Euler's Vault Code Breaker6 min
  10. Quiz5 min
  11. Set the project1 min

By the end you can

  • Find lines of symmetry for 2D geometric shapes.
  • Calculate the order and angle of rotational symmetry.
  • Identify faces, edges, and vertices of 3D solid shapes.
  • Apply Euler's formula F + V - E = 2 to 3D polyhedrons.

Before you start

  • Basic 2D shapes like triangles, squares, and rectangles.
  • Basic 3D shapes like cubes, cylinders, and pyramids.

Have ready

  • Paper, pencil, and a ruler.
  • A small square sheet of paper for folding.

Class 7 · CBSE, ICSE and state boards

Warm-up · think first

A square paper folded in half along a diagonal forms a triangle. How many total lines of symmetry does the original square sheet have?

Show the answer

4 lines of symmetry. A square has 2 diagonal lines and 2 midline lines of symmetry.

Teacher tip: Ask students to fold a square sheet along diagonals and midlines to see all 4 fold lines clearly.

More warm-ups for every class →

🎮 Warm-up games · 5 quick games

Play with Captain Calc

Six minutes with Captain Calc. Vote, say why, then show the answer.

  1. Which shape does not belong based on line symmetry: Square, Rectangle, Circle, Scalene Triangle? (Square · Rectangle · Circle · Scalene Triangle)
    Answer: Scalene Triangle has 0 lines of symmetry, while all the other shapes have at least 2 lines of symmetry.
  2. Would you rather design a hero shield shaped like a regular hexagon (6 lines of symmetry) or a regular octagon (8 lines of symmetry)? (Regular hexagon · Regular octagon)
    Answer: Both choices are great. A regular hexagon has 6 lines of symmetry, while a regular octagon has 8 lines of symmetry.
  3. A cuboid has 6 faces, 8 vertices, and 12 edges. (Always · Sometimes · Never)
    Answer: Always. A cuboid by definition has 6 rectangular faces, 8 corner vertices, and 12 straight edges.
  4. A 3D polyhedron space base has 5 faces and 6 vertices. Using Euler's formula F + V - E = 2, how many edges does it have?
    Answer: 9 edges. Substitute into F + V - E = 2 to get 5 + 6 - E = 2, so 11 - E = 2, giving E = 9.
  5. Where do you see symmetry and 3D solid shapes in real life across India?
    Answer: Examples include spherical domes of monuments, cylindrical steel containers, cubical dice, samosas shaped like triangular pyramids, and symmetric rangoli patterns.

Part 1 of 4 · learn, see, practise

Line Symmetry in 2D Shapes

A line of symmetry divides a shape into two identical mirror halves.

When folded along a line of symmetry, both halves overlap completely.

A regular polygon with n equal sides has exactly n lines of symmetry.

Example 1

How many lines of symmetry does a regular pentagon have?

  1. A regular pentagon has 5 equal sides and 5 equal interior angles.
  2. For any regular polygon, the number of lines of symmetry equals the number of sides.
  3. Therefore, a regular pentagon has 5 lines of symmetry.

Answer: 5

Example 2

How many lines of symmetry does an isosceles triangle have?

  1. An isosceles triangle has two sides of equal length.
  2. A line drawn from the top vertex perpendicular to the base bisects the triangle into two matching halves.
  3. Therefore, an isosceles triangle has exactly 1 line of symmetry.

Answer: 1

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 2
  2. 3
  3. 6
  4. Infinite
  5. 0
  6. 2

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Unlocking the rest of this lesson gives you:

  • Part 2: Rotational Symmetry, with practice at three levels
  • Part 3: 3D Solid Shapes and Their Components, with practice at three levels
  • Part 4: Euler's Formula for Polyhedrons, with practice at three levels
  • Class activity 1: Symmetry Scanner Mission
  • Class activity 2: 3D Base Builder
  • Class activity 3: Euler's Vault Code Breaker
  • A 10-question quiz
  • After-class project: 3D Superhero Command Center Net Designer
  • Homework and a printable practice sheet with answers
  • Teach mode and the minute-by-minute teacher's plan
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FAQ

Symmetry and solid shapes: questions

What is the difference between line symmetry and rotational symmetry?

Line symmetry splits a shape into mirror halves across a fold line. Rotational symmetry means a shape matches itself when rotated around a central point by less than 360°.

Does a cylinder satisfy Euler's formula F + V - E = 2?

No, Euler's formula only applies to polyhedrons with flat polygon faces and straight edges. A cylinder has curved surfaces and curved edges.

How can I quickly remember Euler's formula?

Remember that Faces plus Vertices minus Edges equals 2 (F + V - E = 2), or write it as F + V = E + 2.

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