For a given correspondence of vertices, when corresponding angles of two triangles are congruent, then the two triangles are similar.

SAS Test

For a given correspondence of vertices of two triangles, if two pairs of corresponding sides are in the same proportion and the angle between them are congruent, then the two triangles are similar.

SSS Test

For a given correspondence of vertices of two triangles, when three sides of a triangle are in proportion to corresponding three sides of another triangle, then the two triangles are similar.

Property of three parallel lines and their transversals.

The ratio of the intercepts made on a transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines.