Fold lines and half-turns
Fold line — a line where folding makes the two halves match. Midline — a line joining the midpoints of opposite sides. Half-turn — a turn of 180° about a point. Slanted — a parallelogram with no right angle and no equal neighbouring sides.
A slanted parallelogram turns onto itself, yet no fold line works.
- A square. One diagonal is a fold line.
- The second diagonal folds too.
- Both midlines fold as well. Four fold lines in all.
- A slanted parallelogram has none. A half-turn about O still works.
The rule
Fold along a fold line and the shape fits onto itself. A half-turn can also fit a shape onto itself.
A fold line must fold each corner onto a corner. Only four lines can do that for a four-sided shape. They are the two diagonals and the two midlines.
| Figure | Fold lines | Turns onto itself |
|---|---|---|
| Square | 4 | every quarter turn |
| Rectangle | 2, the midlines | every half turn |
| Rhombus | 2, the diagonals | every half turn |
| Slanted parallelogram (no right angle, no equal neighbouring sides) | 0 | every half turn |
Bisect means cut into two equal parts.
Rule: In every parallelogram the diagonals bisect each other. A half-turn about their crossing swaps each corner with the opposite one. So every parallelogram turns onto itself. A slanted one has no fold line.
Central symmetry — fitting onto itself after a half-turn.
A rectangle that is not a square folds along its midlines only. Its diagonals are equal. But folding along one does not match the halves. A rhombus that is not a square folds along its diagonals only.
Tap how many fold lines each figure has.
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