Question

Explain how the SAS criterion can be used to prove similarity in two triangles.
A. If given a scale factor, you can determine if triangles are similar
B. If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar
C. If all three side lengths are given and proportional to one another, resulting in the same scale factor, then the triangles are similar
D. If at least two angles of the triangles are given and are the same, then the triangles are similar

Answer 1

The SAS (Side-Angle-Side) similarity criterion is a method used to prove that two triangles are similar based on the proportionality of their corresponding sides and the measure of the included angle. According to the SAS criterion, two triangles are similar if:

- Two corresponding sides of one triangle are in proportion to two corresponding sides of another triangle.
- The angles included between these two sides in each triangle are congruent (equal in measure).

Based on the options provided, the correct explanation that aligns with the SAS criterion is:

**B. If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.**

In summary, the SAS criterion confirms similarity when two sides are proportional and the angle between them is equal in both triangles. This leads to the conclusion that the triangles are similar. Options A, C, and D describe other conditions for similarity but do not focus on the SAS criterion specifically.