Fold and fit

About this video

What makes a line a line of symmetry? This animation answers by folding. A heart is folded down the middle, and its right half lands exactly on its left half, edge on edge, with nothing sticking out. That fold is a line of symmetry, also called a mirror line: each half is the mirror image of the other.

A rectangle folds two ways, down the middle and across the middle, so it has two lines of symmetry. Its diagonal is a trap. It does cut the rectangle into two triangles of the same size, but when the rectangle is folded along it, two corners stick out. Two equal halves are not enough: they have to be mirror images across the line.

Then the video counts mirror lines. A square has four: down, across and its two diagonals. An equilateral triangle has three and a regular hexagon six, because every regular polygon has as many mirror lines as sides. A circle has endlessly many, since any line through its centre works. And a parallelogram has none: whichever way you fold it, a corner sticks out. This video goes with the Mirror Lines lesson of Geometry Level 1 on Knaph.

Transcript

1. 0:00Fold a shape along a line. Do the two halves fit?
2. 0:08Fold the heart down the middle.
3. 0:13The halves land exactly on each other. That fold is a line of symmetry.
4. 0:21A rectangle folds two ways. Down the middle, and across.
5. 0:31Now fold along the diagonal.
6. 0:35Equal halves, but corners stick out.
7. 0:37A square has four mirror lines. A triangle with equal sides, three. A regular hexagon, six.
8. 0:51A circle has endlessly many.
9. 0:55And some shapes have none.
10. 0:59If it folds and fits, that line is a mirror line.