A shape or picture has symmetry if one half is the mirror image of the other half.
What is a Line of Symmetry?
- The imaginary line that divides a shape into two equal and identical halves is called the line of symmetry (also called the mirror line).
- If you fold the shape along the line of symmetry, both halves match exactly.
Symmetrical and Non-Symmetrical Shapes
- A square has 4 lines of symmetry.
- A rectangle has 2 lines of symmetry.
- An equilateral triangle has 3 lines of symmetry.
- A circle has infinite lines of symmetry.
- A scalene triangle has 0 lines of symmetry.
Letters with Symmetry
- Letters like A, H, I, M, O, T, U, V, W, X, Y have at least one line of symmetry.
- Letters like B, C, D, E, K have a horizontal line of symmetry.
Drawing the Other Half
To complete a symmetrical drawing, count squares from the mirror line and draw the matching squares on the other side.
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How many lines of symmetry does the letter "H" have?
"H" has 2 lines of symmetry — one horizontal and one vertical.
Does the letter "R" have a line of symmetry?
No, "R" is not symmetrical — the two halves are not mirror images.
A rectangle is 6 cm wide and 4 cm tall. How many lines of symmetry does it have?
A rectangle has 2 lines of symmetry — one along its length and one along its width.
Look at this pattern: | · · · | with the | as the mirror line. What is the reflected pattern?
The other side also has: · · · | — each star appears at the same distance from the mirror line.
A butterfly has wings. Is it symmetrical?
Yes. A butterfly has 1 line of symmetry running down the centre of its body.
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Common mistakes
- Thinking a line that divides into two parts (but not equal mirror halves) is a line of symmetry.
- Forgetting that a circle has infinite lines of symmetry, not just a few.
Summary
Symmetry means both halves are identical mirror images. The dividing line is the line of symmetry. Different shapes have different numbers of lines of symmetry.