Line and rotational symmetry · Usually met around P6
Line symmetry
Fold it: the halves must match exactly.
How to do it
Method
Fold it: the halves must match exactly
Rectangle 2, square 4
Another way
Stand a mirror on it
The half in the mirror matches the other half
In full
A shape that folds along a straight line so the two halves match exactly has line symmetry, and the line is a line of symmetry. To count them, try each fold: the upright middle, the across middle, the diagonals. A rectangle has only 2, upright and across — folded on a diagonal its halves don't match; a square has 4; a regular polygon with n sides has n; a parallelogram has none. To finish a symmetric shape, each point and its partner are the same distance from the line, flipped as in a mirror — not just copied across. Another way: fold paper, or stand a mirror on the line and look.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
How many lines of symmetry does this shape have?
Show the answer and working
Answer: 5 lines
Try every fold — upright, across, slanting: 5 of them match exactly.
Example 2
This shape has line symmetry.
True or false?
Show the answer and working
Answer: False
It has line symmetry only if a fold makes the halves match; this one has 0 lines of symmetry.
Example 3
How many lines of symmetry does a regular polygon with 7 sides have?
Show the answer and working
Answer: 7 lines
A regular polygon's sides and angles are all equal: as many lines of symmetry as sides, 7.
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