All the lines of symmetry

Does a square have only one line of symmetry? Find out by folding a square piece of paper.

• Fold 1: fold it in half vertically, so the left edge meets the right edge.
• Fold 2: fold it in half horizontally, so the top edge meets the bottom edge.

Each time the two halves overlap exactly.

• Fold 3: open it and fold along a diagonal, so that one corner lands on the opposite corner. The halves overlap again!
• Fold 4: fold along the other diagonal. They overlap once more.

No other fold works, so a square has 4 lines of symmetry: the vertical middle line, the horizontal middle line and the two diagonals. A figure can have more than one line of symmetry.

Now take a rectangle that is not a square. Folding it in half vertically or horizontally works: those are 2 lines of symmetry. But fold it along a diagonal and the halves do not overlap: the corners stick out past the edges, because the long sides and short sides are different lengths. So a diagonal of such a rectangle is not a line of symmetry, and the rectangle has only 2 lines of symmetry.