Similar triangles

From Graphic maths
Level: GCSE Maths

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.

Similar-triangles.png

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

See also