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Mathematics
Line and point symmetry
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Drag the shape, move the line and shift the centre to explore reflected images. Overlay the images to recognise a shape's own symmetry.
Drag A to see A′ move
OriginalSymmetric image
Precise adjustment
Arrow keys: 0.1 unit; Shift: 0.5. Home/End and Page Up/Down also work.
A ↔ A′
The points lie on a perpendicular to d, at equal distances from d.
AH = A′H
The image does not coincide for the current line d.
Having a symmetric image does not mean a shape has its own symmetry.
Only the current d/O is tested; all symmetries of a custom triangle are not counted.
Model notes
- The model uses Euclidean plane geometry and arbitrary length units; zoom only changes the view.
- The drag region and minimum distances keep the triangle usable; they are not mathematical limits of symmetry.
- Displayed measurements are rounded. Nearly coincident shapes are not treated as exactly symmetric; the entire shape is compared.
- The folding animation is a projection of a rotating flat sheet; only the final image is measured and tested for symmetry.
- Interactive illustrations do not replace a general proof. Lines and centres of symmetry are listed only for the five fixed shapes.