AA~
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
SAS~
If an angle of one triangle is congruent to an angle of a second triangle and the sides that include the two angles are proportional, then the triangles are similar.
SSS~
If the corresponding sides of two triangles are proportional, then the triangles are similar.
Cross products property
in a proportion, the product of the means equals the product of the extremes.