Symmetry
Line Symmetry
A shape has a line of symmetry if a line divides it into two matching halves. A square has 4 lines of symmetry, a rectangle 2, an equilateral triangle 3, and a circle has many.
Example 1: How many lines of symmetry does a square have?
4 lines of symmetry.
Example 2: How many lines of symmetry does an equilateral triangle have?
3 lines of symmetry.
Quick recap
- A line of symmetry gives two matching halves.
- Square 4, rectangle 2, equilateral triangle 3, circle many.
✓ Quick check
How many lines of symmetry does a rectangle have?
A rectangle has 2 lines of symmetry.
How many lines of symmetry does a circle have?
A circle has infinitely many lines of symmetry.
Rotational Symmetry
A shape has rotational symmetry if it looks the same after turning by some angle less than a full turn. The order is how many times it matches in a full turn, and the angle of rotation is 360° ÷ order. A square has order 4 and angle 90°.
Example 1: What is the order of rotational symmetry of a square?
4.
Example 2: What is the order of rotational symmetry of an equilateral triangle?
3 (angle 120°).
Quick recap
- Order = number of matches in one full turn.
- Angle of rotation = 360° ÷ order.
✓ Quick check
What is the order of rotational symmetry of a rectangle?
A rectangle matches twice in a full turn, so order 2.
The angle of rotation for a shape of order 4 is ___ ?
360° ÷ 4 = 90°.
Reflection Symmetry
Reflection symmetry is when one half is the mirror image of the other across a mirror line. Letters such as H, I, O and X have both vertical and horizontal lines of symmetry, while A has a vertical one.
Example 1: Which letter has both vertical and horizontal symmetry: H or R?
H.
Example 2: A shape with rotational symmetry of order 6 is which regular shape?
A regular hexagon.
Quick recap
- Reflection symmetry mirrors one half onto the other.
- H, I, O, X have both vertical and horizontal symmetry.
✓ Quick check
Which letter has a vertical line of symmetry?
The letter A has a vertical line of symmetry.
A regular hexagon has rotational symmetry of order ___ ?
A regular hexagon has order 6.
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