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Geometry · Quick Reference
Symmetry Cheat Sheet
In one line: symmetry describes when a shape looks exactly the same after being reflected or rotated — a property found throughout nature, art, and architecture.
Key Ideas
1Line Symmetry (Reflectional Symmetry). A shape has line symmetry if it can be folded along a line so that both halves match perfectly; that fold line is called the line of symmetry.
2Number of Lines of Symmetry. Different shapes have different numbers: a square has 4, an equilateral triangle has 3, a circle has infinitely many.
3Rotational Symmetry. A shape has rotational symmetry if it looks the same after being rotated less than a full 360° turn around its center.
4Order of Rotational Symmetry. The number of times a shape matches itself during one full 360° rotation.
5Point Symmetry. A special case of rotational symmetry where a shape looks the same after being rotated exactly 180°.
Worked Examples
How many lines of symmetry does a square have?
4 lines of symmetry
Does the letter 'H' have line symmetry?
Yes, it has both a vertical and a horizontal line of symmetry
Find the order of rotational symmetry for an equilateral triangle.
Order 3
Practice Yourself
How many lines of symmetry does an equilateral triangle have?
3
How many lines of symmetry does a regular pentagon have?
5
Does the letter 'A' typically have a line of symmetry?
Yes, a vertical one
Find the order of rotational symmetry for a square.
4