Recognize Symmetry and Patterns
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What you will learn
- 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. A shape with all sides and angles equal has one line of symmetry for each side: an equilateral triangle has 3, a square has 4, a regular pentagon has 5, and a regular hexagon has 6. 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: one half repeats the other, flipped.
- A square has 4 lines of symmetry: horizontal, vertical, and 2 diagonal.
- A circle has endless 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 slanted parallelogram (not a rectangle or a rhombus) has no line of symmetry, even though it has parallel sides.
Words to know
Symmetry
When a shape has two halves that match exactly
e.g. A heart shape has symmetry.
Line of symmetry
A line that splits a shape into two matching halves
e.g. A square has 4 lines of symmetry.
Pattern
Something that repeats in a regular way
e.g. Red, blue, red, blue is a color pattern.
Mirror image
A reflected match — what you see in a mirror
e.g. The two halves are mirror images.
Repeat
To show the same thing again
e.g. The shape pattern repeats every 3 squares.
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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