Lines of Symmetry

Fold a shape along a line. If the halves match exactly, that line is a line of symmetry.

That fold line has a name.

Line of symmetry is a line that splits a shape into two matching halves.

How many there are

A square has 4. A rectangle has 2. A circle has more than anyone can count.

Some shapes have none

No fold makes the halves of a scalene triangle match.

A fold that makes the halves match

A line of symmetry is a fold line where one half lands exactly on the other. Not roughly — exactly. Testing with real paper is the most convincing way to check, and it settles arguments that eyeballing cannot.

How many lines a shape has

A square has 4 lines of symmetry, a rectangle 2, an equilateral triangle 3, and a circle infinitely many. A scalene triangle has none. The count is a property of the shape, and it is often a good clue to what the shape is.

A rectangle's diagonal is not a line of symmetry

Fold a non-square rectangle along its diagonal and the halves do not match — they are the right area but the wrong shape. This surprises almost everyone. It is another case where you must test rather than assume.

Symmetry outside maths

Butterflies, faces, letters like A and M, and most buildings are roughly symmetrical. Designers use symmetry because it reads as balanced. Looking for lines of symmetry in the world is a good way to make the idea stick.