Symmetry

Identify lines of symmetry in shapes

Symmetry

What is Symmetry?

Symmetry means a shape looks the same on both sides when you fold it or flip it.

Think of a butterfly - if you draw a line down the middle, both sides look the same!

Line Symmetry (Reflection Symmetry)

Line of symmetry: An imaginary line where you can fold a shape and both halves match perfectly.

Examples:

  • A heart has 1 line of symmetry (vertical)
  • A rectangle has 2 lines of symmetry (horizontal and vertical)
  • A square has 4 lines of symmetry
  • A circle has infinite lines of symmetry!

How to find lines of symmetry:

  1. Imagine folding the shape
  2. If both halves match exactly, you found a line of symmetry
  3. Try folding different ways

Shapes and Their Lines of Symmetry

No lines of symmetry:

  • Scalene triangle (all sides different)
  • Most letters (like F, G, J, L, N, P, Q, R, S, Z)

1 line of symmetry:

  • Isosceles triangle
  • Letters A, B, C, D, E, M, T, U, V, W, Y

2 lines of symmetry:

  • Rectangle

3 lines of symmetry:

  • Equilateral triangle

4 lines of symmetry:

  • Square

Many lines of symmetry:

  • Regular pentagon (5 lines)
  • Regular hexagon (6 lines)
  • Circle (infinite)

Rotational Symmetry

Rotational symmetry: When you can turn (rotate) a shape and it looks the same before you turn it all the way around.

Examples:

  • A square has rotational symmetry - turn it 90° and it looks the same
  • A rectangle has rotational symmetry - turn it 180° and it looks the same
  • A five-pointed star has rotational symmetry

Real-World Symmetry

Nature:

  • Butterfly wings
  • Flowers (like daisies)
  • Snowflakes
  • Leaves

Man-made:

  • Road signs (stop sign has 8 lines!)
  • Buildings
  • Logos
  • Decorative patterns

Practice Tips

To check for symmetry:

  1. Use a mirror - place it on the shape
  2. If the mirror reflection completes the shape, that's a line of symmetry
  3. Try the mirror in different positions

Drawing symmetric shapes:

  1. Draw one half
  2. Fold your paper on the line of symmetry
  3. Trace the shape to make the other half
  4. Unfold to see your symmetric shape!

Common Mistakes

❌ Thinking all shapes have symmetry (they don't!) ❌ Forgetting to check all possible lines ❌ Confusing line symmetry with rotational symmetry

✅ Remember: Line symmetry = fold and match ✅ Rotational symmetry = turn and it looks the same

📚 Practice Problems

1Problem 1easy

❓ Question:

Does the letter "H" have line symmetry? If yes, how many lines of symmetry does it have?

💡 Show Solution

Yes! The letter "H" has 2 lines of symmetry:

  1. A vertical line down the middle (splits it into left and right halves)
  2. A horizontal line across the middle (splits it into top and bottom halves)

Both halves match perfectly when you fold along these lines! ✓

2Problem 2medium

❓ Question:

Draw all lines of symmetry for a square.

💡 Show Solution

A square has 4 lines of symmetry:

  1. Vertical line through the center (top to bottom)
  2. Horizontal line through the center (left to right)
  3. Diagonal line from top-left to bottom-right
  4. Diagonal line from top-right to bottom-left

All 4 lines divide the square into matching halves! ✓

3Problem 3easy

❓ Question:

Which capital letters have exactly 1 line of symmetry: A, B, C, or D?

💡 Show Solution

The letters with exactly 1 line of symmetry are:

  • A - 1 vertical line of symmetry ✓
  • B - 1 horizontal line of symmetry ✓
  • C - 1 horizontal line of symmetry ✓
  • D - 1 horizontal line of symmetry ✓

All four letters have exactly 1 line of symmetry!

4Problem 4hard

❓ Question:

Does a circle have rotational symmetry? How many times does it match itself in one full turn?

💡 Show Solution

Yes! A circle has rotational symmetry.

It matches itself infinite times during one full turn!

No matter how much you rotate a circle, it always looks exactly the same. Every point on the circle is the same distance from the center.

This is called "infinite rotational symmetry" ✓

5Problem 5medium

❓ Question:

Complete this symmetrical shape: If the left half shows a triangle with base 4 cm, what should the right half show?

💡 Show Solution

The right half should show:

An identical triangle with base 4 cm

For line symmetry, both sides must be mirror images:

  • Same shape (triangle)
  • Same size (4 cm base)
  • Same position relative to the line of symmetry
  • Flipped/reflected across the line

The completed shape would be a larger triangle or a diamond/kite shape made of two triangles! ✓

🎴

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