After sorting shapes, here is one more attribute to look for: does the shape have a mirror line?
Key idea
A line of symmetry folds a shape so the two halves match exactly. A rectangle has 2 (across its middles), a square has 4, an equilateral triangle has 3, and some shapes have none.
Why it works
Folding along a line flips each point to the same distance on the other side. A line is a line of symmetry only if every corner lands exactly on another corner. For a rectangle's diagonal, the corners land outside the rectangle, so the diagonal is not a line of symmetry.
Worked example: Count the lines
How many lines of symmetry does a square have?
- Fold across the middle up-and-down and side-to-side: 2 lines.
- Fold along each diagonal: the corners match, 2 more lines.
Answer: 4
Worked example: Test a line
Is the line from the top corner of an isosceles triangle to the middle of its base a line of symmetry?
- The two equal sides fold onto each other.
- The base's halves match, and the top corner stays on the line.
Answer: Yes
Common mistake
Drawing a diagonal of a rectangle as a line of symmetry. A diagonal cuts the rectangle into two equal triangles, but folding along it does not make them match. Equal halves are not enough; the fold must line them up.