8.3+(winbr5)

AA (Angle - Angle) Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

SSS (Side - Side - Side) Similarity Theorem
If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar

SAS ( Side - Angle - Side) Similarity Theorem
If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent then the triangles are similar.

Examples
//the picture above is an example of how triangles can fit in to one another//

QR/UT equals 4/2.4 equals 5/3 RS/TV equals 7/4.2 equals 5/3 QS/UV equals 7/4.2 = 5/3 The sides of the triangle are proportional by SSS similarity so triangle QRS is congruent to triangle UTV.
 * SSS**

GF/XY equals 3/2 GH/XZ equals 5.4/3.6 equals 3/2 The included angles of these sides are congruent and the sides of the triangle are proportional. triangle QRS is congruent to triangle UTV by SAS theorem.
 * SAS**

This triangle has two angle that are given on points D and B. That means that the line connecting B and D is the same size. So triangle BCD is congruent to triangle BED these triangles are congruent by ASA.
 * ASA**