Does It Look the Same — Class 5 Mathematics (CBSE)
Based on the NCERT Math Magic Grade 5 textbook. Explore symmetry in shapes and patterns, then solve the practice set without looking at the answers.
1. Why this chapter matters
Symmetry is everywhere — in butterfly wings, human faces, buildings, and traditional Indian rangoli patterns. This chapter introduces two types of symmetry: mirror symmetry (reflection) and rotational symmetry (turn). Students learn to identify symmetrical shapes, find lines of symmetry, and understand how shapes look after quarter, half, and full turns. This builds spatial reasoning and an appreciation for patterns in art and nature.
2. Mirror halves (line symmetry)
A shape has mirror symmetry if it can be folded into two identical halves that match exactly. The fold line is called the line of symmetry (or mirror line).
Examples of mirror symmetry
| Object | Number of lines of symmetry | Description |
|---|---|---|
| Square | 4 | Two diagonals, one vertical, one horizontal |
| Rectangle | 2 | One vertical, one horizontal |
| Circle | Infinite | Any line through the centre |
| Equilateral triangle | 3 | From each vertex to the opposite side |
| Butterfly | 1 | Vertical line through the body |
| Human face (ideal) | 1 | Vertical line down the centre |
Checking for mirror symmetry
- Draw the shape on paper.
- Draw a line where you think the mirror line might be.
- Fold the paper along the line. If both halves match exactly, the line is a line of symmetry.
3. Making symmetric shapes
To make one half of a symmetric shape:
- Draw one half of a shape on one side of a line.
- Place a mirror on the line. The reflection shows the complete shape.
- Trace the reflection to complete the shape.
Activity: Write your name on a piece of paper. Hold it up to a mirror. Which letters look the same in the mirror? Which letters change?
Letters with line symmetry
- Vertical line of symmetry: A, H, I, M, O, T, U, V, W, X, Y
- Horizontal line of symmetry: B, C, D, E, H, I, K, O, X
- No line of symmetry: F, G, J, L, N, P, Q, R, S, Z
4. Rotational symmetry
A shape has rotational symmetry if it looks the same after a turn of less than 360 degrees (one full turn). The centre point around which the shape rotates is called the centre of rotation.
Types of turns
| Turn | Fraction of full turn | Degrees | Example |
|---|---|---|---|
| Quarter turn | 1/4 turn | 90° | A square rotated by 90° |
| Half turn | 1/2 turn | 180° | A rectangle rotated by 180° |
| Three-quarter turn | 3/4 turn | 270° | A square rotated by 270° |
| Full turn | 1 turn | 360° | Any shape returns to original position |
Order of rotational symmetry
The order tells how many times a shape looks the same during one full rotation.
| Shape | Order of rotational symmetry | Turns that match |
|---|---|---|
| Square | 4 | 90°, 180°, 270°, 360° |
| Rectangle | 2 | 180°, 360° |
| Equilateral triangle | 3 | 120°, 240°, 360° |
| Circle | Infinite | Any turn |
| Regular hexagon | 6 | 60°, 120°, 180°, 240°, 300°, 360° |
5. Rangoli patterns
Rangoli is a traditional Indian art form where patterns are created on the floor using coloured powders, rice, or flowers. Rangoli designs often use both mirror symmetry and rotational symmetry.
Creating symmetric rangoli designs
Method 1 (mirror symmetry):
- Fold a paper into two halves.
- Cut a design along the fold.
- Open the paper — the design is symmetric on both sides.
Method 2 (rotational symmetry):
- Fold a paper into four equal parts (by folding twice).
- Cut a design through all layers.
- Open the paper — the design has 4-fold rotational symmetry.
Examples of symmetric rangoli: A flower with four petals around a centre point has rotational symmetry of order 4. A diya pattern mirrored left and right has line symmetry.
6. Which shapes look the same after a turn?
| Shape | After 1/4 turn | After 1/2 turn | After 3/4 turn | After full turn |
|---|---|---|---|---|
| Square | Same | Same | Same | Same |
| Rectangle | Different | Same | Different | Same |
| Equilateral triangle | Different | Different | Different | Same |
| Circle | Same | Same | Same | Same |
Note: For Class 5, focus on identifying whether a shape looks the same after 1/2 turn (180°) and 1/4 turn (90°).
7. Activity corner
Activity 1: Collect five leaves from your garden. Check whether each leaf has line symmetry. Draw the line of symmetry on each leaf.
Activity 2: Cut out a square from paper. Mark one corner with a dot. Rotate the square by 1/4 turn, 1/2 turn, 3/4 turn, and full turn. After which turns does the dot return to its original position?
Activity 3: Draw a simple rangoli pattern (a flower with 4 petals) on a square grid. Colour it symmetrically.
8. Common mistakes
- Mistake: Thinking every shape has at least one line of symmetry Fix: Many shapes (like an irregular quadrilateral or a scalene triangle) have no line of symmetry. Check by folding.
- Mistake: Confusing mirror symmetry with rotational symmetry Fix: Mirror symmetry = folding. Rotational symmetry = turning. They are different concepts.
- Mistake: Saying a shape looks the same after any turn Fix: Test each turn separately. A rectangle does NOT look the same after a 1/4 turn, only after a 1/2 turn.
9. Key facts
- A shape has line symmetry if it can be folded into two matching halves.
- The fold line is called the line of symmetry.
- A shape has rotational symmetry if it looks the same after a turn of less than 360°.
- The order of rotational symmetry is the number of matching positions in one full turn.
- A square has 4 lines of symmetry and rotational symmetry of order 4.
- Rangoli patterns often use both types of symmetry.
- Not all shapes are symmetric.
10. Self-test
- How many lines of symmetry does a square have?
- Does a rectangle look the same after a 1/4 turn? Explain.
- What is the order of rotational symmetry of an equilateral triangle?
- Name two letters that have vertical line symmetry.
- Why does a circle have infinite lines of symmetry?
11. Answer key
-
How many lines of symmetry does a square have? Answer: A square has 4 lines of symmetry — two along the diagonals, one vertical, and one horizontal through the centre.
-
Does a rectangle look the same after a 1/4 turn? Explain. Answer: No. After a 1/4 turn (90°), the rectangle becomes vertical instead of horizontal. It only looks the same after a 1/2 turn (180°) or full turn (360°).
-
What is the order of rotational symmetry of an equilateral triangle? Answer: Order 3. It looks the same after 120°, 240°, and 360° turns.
-
Name two letters that have vertical line symmetry. Answer: A, H, I, M, O, T, U, V, W, X, Y (any two from these).
-
Why does a circle have infinite lines of symmetry? Answer: Any line passing through the centre of a circle divides it into two identical halves. Since there are infinite lines through the centre, the circle has infinite lines of symmetry.
12. Quick revision
- Mirror symmetry: shape looks same when folded along a line.
- Rotational symmetry: shape looks same when turned by less than 360°.
- Check symmetry by folding or using a mirror.
- Rangoli patterns use both types of symmetry.
- Practise with paper folding and cutting to understand symmetry.
- Observe symmetry in nature — leaves, flowers, butterflies, snowflakes.
