Geometry
GradesGrade 4GeometryLines of Symmetry

Lines of Symmetry

📐 Geometry
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Lines of Symmetry

A line of symmetry divides a shape into two mirror-image halves!

A LINE OF SYMMETRY is a line that divides a figure into two halves that are exactly the same — one is the mirror image of the other. We say the shape has REFLECTIVE SYMMETRY. Some shapes have many lines of symmetry; others have none!

Lines of symmetry in common shapes:

Square: 4 lines of symmetry (2 through midpoints, 2 through corners)Rectangle: 2 lines of symmetry (through midpoints only)Equilateral triangle: 3 lines of symmetryCircle: infinite lines of symmetry!Scalene triangle: 0 lines of symmetry

Regular polygons (all sides and angles equal) have the most lines of symmetry.

Symmetric letters

A (vertical)H (vertical + horizontal)O (infinite)M (vertical)

Asymmetric letters

FGJLPQR

You can test letters of the alphabet for symmetry too — it is great practice!

How to check if a line is a line of symmetry:

1Fold the shape (or imagine folding it) along the line
2If both halves match EXACTLY — same shape, same size — it IS a line of symmetry
3If they do not match (one side is bigger or differently shaped), it is NOT
🦋Butterfly wings
A butterfly's wings are a perfect example of symmetry.
Draw a vertical line down the center of the butterfly.
The left wing is a mirror image of the right wing.
That vertical line is the butterfly's line of symmetry!
A regular n-gon has exactly n lines of symmetry.\text{A regular } n\text{-gon has exactly } n \text{ lines of symmetry.}
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Remember This!

Not all lines through a shape are lines of symmetry! A diagonal through a non-square rectangle does NOT create matching halves — try folding to check!

✏️ Try It!

How many lines of symmetry does a regular hexagon have?

Take Quiz 📝 — 25 Questions