Lines of symmetry

The book shows a blue triangle with a dotted line going straight down from its top corner to the middle of its bottom side. If you fold the triangle along that dotted line, one half covers the other half completely. Two halves like these are called mirror halves.

Next to it are four puzzle pieces fitted together, with a dotted line through the middle. Are the two sides mirror halves? No. The puzzle pieces have knobs and gaps in different places, so when you fold along the line, the left half does not exactly fit over the right half.

A line that cuts a figure into two parts that exactly overlap when folded along that line is called a line of symmetry of the figure. (You may also hear it called an axis of symmetry.) To test a line, imagine folding along it: if every part on one side lands exactly on a part on the other side, it is a line of symmetry. If anything sticks out or is left uncovered, it is not. You can make one in art class: put blobs of paint on one half of a sheet, fold, press and open. The two halves match, and the fold is the line of symmetry.

Some figures have no line of symmetry at all. A cloud, for example, cannot be folded along any line so that its two parts match.