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Section 8.3 · Geometry and measure

Symmetry

Identify line symmetry and rotational symmetry in 2D shapes, and state the order of rotational symmetry.

6 teaching slides 52 practice questions Worked answers for every question

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2 · Key words

line of symmetryA line the shape folds along so the halves match.
reflective symmetrySymmetry about a line; also called line symmetry.
rotational symmetryLooking the same after a turn about a point.
order of rotational symmetryHow many times a shape looks the same in one full turn.
centre of rotationThe point the shape is turned about.

3 · Summary of the sectionrevise from this

  • A line of symmetry is a fold line: the two halves match exactly.
  • The order of rotational symmetry is how many times a shape looks the same in one full turn.
  • The smallest turn that works is 360 ÷ order.
  • The smallest possible order is 1, not 0 — every shape returns to itself after a full turn.
  • A regular n-gon has exactly n lines of symmetry and order n.
  • The two kinds of symmetry are independent: a parallelogram has no lines but order 2.
  • A circle has infinitely many lines and infinite order.
  • Check a fold line by imagining the paper folded — “it looks about right” is not enough.
PDFPrintable worksheet All 52 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Math Antics - Points, Lines, & Planes

American stretchmathantics

The vocabulary that sits underneath every shape question.

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4 · Practice52 questions, easiest first

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8.2 The parts of a circle
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8.4 3D shapes and nets