Symmetry · Usually met around P3
Symmetric shapes and lines of symmetry
Fold on the line: the halves must match exactly.
How to do it
Method
Fold on the line: the halves must match exactly
A matches folded upright, not across: 1 line
Another way
Stand a mirror on it
The half in the mirror matches the other half → a line of symmetry
In full
A shape that folds along a straight line so that the two halves match exactly is symmetric, and the fold is its line of symmetry. To check, imagine folding on the line and compare point by point: every point on one side needs a partner just as far from the line on the other side. A line of symmetry can be upright, flat or slanting; some shapes have more than one, some have none. The capital letters A, M and T have an upright line; B, C and E a flat one; H, I, O and X both; F, G and L none. On a flag or a pattern the colours must match after folding too. Another way: stand a mirror on the line. If the half you see in the mirror is exactly the other half on the paper, the line is a line of symmetry.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The dashed line is a line of symmetry of this letter.
True or false?
Show the answer and working
Answer: True
Fold on the dashed line: only if the squares on the two sides match exactly is it a line of symmetry.
Example 2
How many lines of symmetry does this flag have (the colours must match too)?
Show the answer and working
Answer: 0 lines
Try each fold: the upright and flat middles, and on a square flag the diagonals too. Shape and colours match on 0 of them.
Example 3
What lines of symmetry does this letter have?
- A. None
- B. Only a flat one
- C. Both an upright and a flat one
- D. Only an upright one
Choose the right answer
Show the answer and working
Answer: A. None
Folded on the upright middle, left matching right means an upright line; folded on the flat middle, top matching bottom means a flat one.
Practise it in the game →Symmetry · Free to start, unlimited questions, no download