Question

Describe what information would be needed if you wanted to prove triangle BAC~triangle DFE. Be specific with side lengths, angle names and the postulate that you use. PLEASE MAKE IT SIMPLE!!! I've tried to ask this question before but it ended in mass confusion!

Answer 1

Refer to my drawing . Unlike most textbook problems, the triangles were drawn to scale. Side lengths 2a and side 2b are indeed proportional to side lengths a and b, respectively. It is obvious that the triangles are not similar. This is a counterexample that proves SS Similarity does not hold true. 

There is no SS Similarity. 

There is SAS Similarity. 

To prove two triangles similar you need one of the following three situations: 

1. The lengths of three sides of one triangle proportional to lengths of the three sides of the other triangle. (SSS Similarity Theorem) 

2. Two angles of one triangle congruent to two angles of another triangle. (AA SImilarity Theorem) 

3. The lengths of two sides of one triangle proportional to the lengths of two sides of another triangle, and their included angles congruent. (SAS Similarity Theorem)