Unit 7 · Topic 05 · Geometry
Anaya folded a paper butterfly in half and both wings landed exactly on top of each other.
Kabir folded the letter F the same way, and nothing matched at all.
One fold worked because of a fact the shape itself was hiding: symmetry.
Ms. Rao handed out paper cutouts: a butterfly, a heart, the letter A, and the letter F. "Fold each one so both halves match exactly. If you can, mark the fold line."
Anaya folded the butterfly right down the middle. The two wings lined up perfectly — every dot, every curve.
"That fold line is called a line of symmetry," said Ms. Rao. "When a shape folds onto itself with no part sticking out or missing, that fold is a line of symmetry, and the shape is symmetric across it."
Kabir tried the heart the same way. It also folded perfectly down the centre. Then he tried the letter A — top point folded straight down, both legs matched. "A has one too!"
He picked up the letter F and folded it every way he could think of — down the middle, sideways, diagonally. Nothing matched. "F has no fold that works at all."
"Exactly right," said Ms. Rao. "Not every shape has a line of symmetry, and that's fine — F genuinely has none. But some shapes have MORE than one."
She handed Anaya a square. Anaya found the vertical fold worked. Then the horizontal fold also worked. Then, surprising herself, both diagonals worked too. "Four lines of symmetry, in one square!"
"A square is one of the most symmetric ordinary shapes there is," said Ms. Rao. "A rectangle that isn't a square only has two — the vertical and horizontal, not the diagonals, because the diagonals don't match up when the sides are different lengths."
Kabir tested a circle by folding it every possible way. "Every single fold through the centre works!" "A circle has infinite lines of symmetry — through its centre, in any direction," said Ms. Rao.
By the end, the class had sorted every shape and letter into three piles: no line of symmetry (like F, and the letter R), exactly one (like the heart and the letter A), and more than one (like the square and the circle).
A line of symmetry is a fold line where a shape folds exactly onto itself — both halves match perfectly, with nothing sticking out or missing.
A shape can have zero lines of symmetry (like the letters F, G, J), exactly one (like the letter A, or a heart), or more than one (like a square, which has 4, or a circle, which has infinitely many).
A square has 4 lines of symmetry: vertical, horizontal, and both diagonals. A non-square rectangle has only 2 (vertical and horizontal) — the diagonals don't match because the sides are unequal lengths.
The reliable test for any shape: physically fold it (or imagine folding it) and check if every point on one side lands exactly on a matching point on the other side.
Fold paper cutouts of the letters A, B, E, F, N and check which ones have a line of symmetry.
Draw a square, a rectangle and a circle, and mark every line of symmetry you can find on each.
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