Final answer:
The SAS Similarity postulate does not exist for proving triangles similar, it's a common misconception due to the presence of an SAS postulate for proving triangle congruence. The correct postulates for proving triangle similarity are AAA, AA, and SSS.
Step-by-step explanation:
The postulate that is not used to prove triangles similar is the SAS (Side-Angle-Side) Similarity postulate. While there are several postulates and theorems that allow us to prove the similarities between triangles, SAS Similarity is not one of them. However, it's worth noting that there is an SAS postulate for proving triangles congruent, which might lead to some confusion.
The correct postulates for proving triangle similarity are:
- AAA (Angle-Angle-Angle): If all three angles in one triangle are congruent to the corresponding angles in another triangle, the triangles are similar.
- AA (Angle-Angle): If two angles in one triangle are congruent to the corresponding angles in another triangle, the triangles are similar.
- SSS (Side-Side-Side): If the corresponding sides of two triangles are in proportion, the triangles are similar.
It is important to remember that while the SSS and SAS postulates are used for proving congruency (exact matching of all sides and angles), only the SSS and AA postulates can be used for similarity (matching of angles and relative proportion of sides).