How do we complete similarity proofs?

There are 3 type of Similarity proof postulates which are:

1. AA
2. SAS
3. SSS

AA

To show two triangles are similar, it is sufficient to show that two angles of one triangle are congruent (equal) to two angles of the other triangle.

If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.   SSS for similarity BE CAREFUL!!  SSS for similar triangles is NOT the same theorem as we used for congruent triangles. To show triangles are similar, it is sufficient to show that the three sets of corresponding sides are in proportion. Theorem: If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.   SAS for similarity BE CAREFUL!!  SAS for similar triangles is NOT the same theorem as we used for congruent triangles.  To show triangles are similar, it is sufficient to show that two sets of corresponding sides are in proportion and the angles they include are congruent. Theorem: If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. All of the similarities are found to be in proportions Dealing with overlapping triangles:    Many problems involving similar triangles have one triangle ON TOP OF  (overlapping) another triangle.  Since is marked to be parallel to , we know that we have <BDE congruent to <DAC (by corresponding angles).  <B is shared by both triangles, so the two triangles are similar by AA.   Additional Theorem: If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, the line divides these two sides proportionally. Guided Practice: 1)Which postulate is used to answer this?    Citations:  http://www.regentsprep.org/regents/math/geometry/GP11/LsimilarProof.htm  http://www.regentsprep.org/regents/math/geometry/GP11/PracSimPfs.htm