Recognize Symmetry and Patterns
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Learning Objectives
- 1Identify shapes that have lines of symmetry
- 2Distinguish between symmetrical and non-symmetrical shapes
Mini Lesson
A shape has a line of symmetry if it can be folded exactly in half so both sides match perfectly. Shapes like squares, circles, and equilateral triangles have lines of symmetry. Some shapes — like a scalene triangle or the letter Z — have no line of symmetry because no fold makes both sides match.
What Is a Line of Symmetry?
- A line of symmetry divides a shape into two mirror-image halves.
- A square has 4 lines of symmetry: horizontal, vertical, and 2 diagonal.
- A circle has infinitely many lines of symmetry — any line through its center works.
- A rectangle has 2 lines of symmetry: horizontal and vertical only.
Shapes with No Line of Symmetry
- A scalene triangle has three sides all of different lengths — no fold creates equal halves.
- An irregular quadrilateral (four unequal sides and angles) has no symmetry.
- The letters Z and S have no line of symmetry — they look different when flipped.
- A parallelogram (not a rectangle) has no line of symmetry despite having parallel sides.
To test for symmetry, imagine folding the shape along a line. If both halves match exactly, that line is a line of symmetry.
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