Refresher - Similarity Between Triangles

How to tell if triangles are similar

Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are similar. Various groups of three will do. Triangles are similar if:

1. AAA (angle angle angle)
   All three pairs of corresponding angles are the same.
2. SSS in same proportion (side side side)
   All three pairs of corresponding sides are in the same proportion
3. SAS (side angle side)
   Two pairs of sides in the same proportion and the included angle equal.

Similar Triangles can have shared parts

Two triangles can be similar, even if they share some elements. In the figure below, the larger triangle PQR is similar to the smaller one STR. S and T are the midpoints of PR and QR respectively. They share the vertex R and part of the sides PR and QR. They are similar on the basis of AAA, since the corresponding angles in each triangle are the same.