This chapter studies symmetry, where parts of a figure repeat in a definite pattern. A line of symmetry (or axis of symmetry) is a line that cuts a figure into two parts that exactly overlap when folded along it; the parts are mirror halves and the figure has reflection symmetry. A figure may have several lines of symmetry: a square has 4, an equilateral triangle has 3, and a circle has infinitely many \u2014 every diameter is a line of symmetry. The chapter shows how to generate symmetric shapes by ink-blots, paper folding and cutting, and hole punching. It then introduces rotational symmetry: a figure has rotational symmetry if it looks exactly the same after being rotated by some angle, less than \(360^\circ\), about a fixed centre of rotation. Such an angle is an angle of symmetry, and \(360^\circ\) is always one. The angles of symmetry are multiples of the smallest one, which (when a whole number) is a factor of \(360\); for figures with radial arms, equally spaced arms of \(360^\circ/n\) give \(n\) angles of symmetry. A figure may have lines of symmetry, angles of symmetry, both, or neither.
Line of SymmetryFigures with Many Lines of SymmetryReflection and Generating Symmetric ShapesRotational SymmetryAngles and Centre of RotationSymmetries of a Circle
Key terms
Symmetry
A property where parts of a figure repeat in a definite pattern.
Line of symmetry
A line that divides a figure into two parts that exactly overlap when folded along it; also called an axis of symmetry.
Reflection symmetry
The symmetry a figure has when it possesses one or more lines of symmetry.
Rotational symmetry
The property of looking exactly the same after a rotation of less than \(360^\circ\) about a fixed point.
Angle of symmetry
An angle through which a figure can be rotated to look exactly the same.
Centre of rotation
The fixed point about which a figure is rotated.
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A line that divides a figure into two parts that exactly overlap when folded is called a
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