Lines, angles & symmetry
The idea
Fold a paper heart in half and the two sides match perfectly — that fold line is called a line of symmetry, and finding them is one of three closely related ideas. A line is a perfectly straight path; when two lines or sides meet at a corner, the amount of turn between them is an angle. A square corner, like the corner of a book, is called a right angle; smaller openings are sharp and pointy, wider ones are more open.
Two honest tests keep these ideas trustworthy. For angles: the size of an angle is the size of the opening, not the length of the sides drawn. Two short pencils opened wide make a bigger angle than two long rulers opened barely at all — a very common mix-up. For symmetry: fold the shape, or imagine folding it, and see whether the halves land exactly on each other. Eyes can be fooled by halves that merely look the same size, but the fold test never lies.
Worked example
Take a paper rectangle that is longer than it is wide, like a postcard. How many lines of symmetry does it have? Test folds across the middle both ways and a fold along a diagonal.
- Remember what a line of symmetry is: a fold line where the two halves land exactly on top of each other. Folding is the honest test, so try each fold.
- Fold the postcard in half the short way, edge meeting edge: the two halves match perfectly. That middle fold is one line of symmetry.
- Fold it in half the long way: the halves match again, so that is a second line of symmetry.
- Now fold corner to corner along a diagonal. The two triangle halves are the same size, but they do not land on each other — corners poke out past the edges — so the diagonal fails the fold test.
- Count the folds that worked: only the two middle ones. A stretched rectangle has exactly 2 lines of symmetry; only a square earns 4.
Answer. A non-square rectangle has exactly 2 lines of symmetry — the two middle folds, never the diagonals.
Check your understanding
- Why does the fold test settle whether a line really is a line of symmetry?
- What makes one angle bigger than another — longer sides or a wider opening — and how could you check with two pencils?
- Which capital letters of the alphabet have a line of symmetry, and where does each fold go?
- Why does a square have more lines of symmetry than a stretched rectangle?