Write each of the results and compare them. What are they used for? How do you choose which result to use?
See solution.
Practice makes perfect
Let's begin by writing the three results to be compared.
Angle-Angle (AA) Similarity Postulate
If two angles of one triangles are congruent to two angles of another triangle, then the triangles are congruent.
Side-Side-Side (SSS) Similarity Theorem
If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
Side-Angle-Side (SAS) Similarity Theorem
If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are congruent.
As we can see, the three results written above can be used to determine whether two triangles are similar. However, the theorem to be used depends on the given information.
