Similar shapes

From Graphic maths
Level: GCSE Maths

Two shapes are similar if they are the same shape. They don't need to be the same size. These three shapes are similar:

Similar-poly.png

All three shapes are similar, because they are the same shape.

Similar polygons

Two polygons are similar if

  • all their corresponding angles are equal.
  • all their corresponding sides are proportional.

For example all regular hexagons are similar. If you take a regular hexagon and double the length of every side, it is still a regular hexagon because each side has changed by the same amount (shapes A and B below).

If you take a regular hexagon and just double just two sides, it is no longer similar, even though it still has the same angles (shape C).

Dissimilar-square.png

Triangles

For similar triangles there are special rules.

Other shapes

Other shapes can be similar. For example, all circles are similar, even if they do not have the same radius.

See also