Symmetry
Line symmetry
Find the lines of symmetry of shapes and letters, and tell a mirror line from a line that only looks like one.
A shape has a line of symmetry if folding along that line lays the two halves exactly on top of each other. The line is a mirror: everything on one side of it has a matching part the same distance away on the other side. Some shapes have no such line, some have one, and a regular shape has as many as it has sides.
Cutting a shape in half is not enough
A line can split a shape into two equal areas without being a line of symmetry at all. The diagonal of a rectangle that is not a square makes two identical triangles, but folding along it puts a long side on top of a short one, so it is not a mirror line. The test is always the fold, never the area.
Worked example
How many lines of symmetry does the capital letter E have?
Fold it left onto right. The three arms end up pointing the wrong way, so that fails.
The letter is not the same on its left and its right — all three arms are on one side.
Try it together
Now let us work out the lines of symmetry of a regular decagon and of the capital letter T.
One of these follows a rule, and the other has to be tested by folding.
1.How many sides does a decagon have?
Have a go
Have a go on your own: how many lines of symmetry does a regular heptagon have?
Hint: A heptagon has seven sides.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.