Two triangles are similar if they are the same shape, but not necessarily the same size. This means that:
- all their corresponding angles must be equal
- all their corresponding sides must be proportional (see below)
Rules for similar triangles
In the diagram, A, B and C are all similar. They all have the same angles,and their sides are proportional.
What do we mean by proportional? Well, for example, triangle B is twice as big as triangle C. Each side in triangle B is twice as long as the equivalent side in triangle C. Since each side is scaled up by the same amount, we say they are proportional.
For triangles, it is not always necessary to prove that every side and angle is the same. There are several shortcuts you can use. Two triangles are congruent if:
- All three angles match up
- If all three sides are proportional
- Two sides are proportional, and the angle between them matches