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.So the scale factor equals 9/5 = 1.8

So side AB = 3 x 1.8 = 5.4 cm