Similar Triangles and Similar Shapes

Similar shapes are exactly the same shape…but can be different sizes. This means all their angles must be the same and their sides proportional to each other.

Similar Triangles

Two triangles are similar if any of the following are true:

  • All their angles are equal
  • All sides are proportional (e.g. if one has sides 2cm, 3cm and 5cm and the other has sides 4cm, 6cm and 10cm). This means there is a constant “scale factor”
  • Any two sides are proportional and the angle between them is equal

Like with triangle enlargements, to work out a scale factor you need to divide a side on the new shape by the same side on the old shape. You can then use this to find other sides.

Example: Triangles ABC and DEF are similar. Find the length of side AC.similar triangles exampleSo the scale factor equals 9/5 = 1.8

So side AB = 3 x 1.8 = 5.4 cm