Triangles are considered similar by the angle-angle (AA) criterion if two angles of one triangle are equal to two angles of another triangle. This means that if you can show that two corresponding angles in two different triangles are equal, the third angles must also be equal due to the properties of triangles. Therefore, the two triangles are similar.
For example, if you have triangle ABC and triangle DEF, and you know that angle A equals angle D and angle B equals angle E, then by the AA criterion, triangle ABC is similar to triangle DEF. This similarity means that the triangles have the same shape but may differ in size. As a result, the corresponding sides of the triangles are in proportion.
It’s important to note that this criterion doesn’t require knowledge of the lengths of the sides of the triangles, only the measures of the angles. This makes it a very useful tool for proving similarity in geometric problems.