Question

explain how the sas criterion can be used to prove similarity in two triangles. (1 point)

• if all three side lengths are given and proportional to one another, resulting in the same scale factor, then the triangles are similar.
• if at least two angles of the triangles are given and are the same, then the triangles are similar.
• if two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.
• if given a scale factor, you can determine if triangles are similar.

Explanation:

The SAS (Side - Angle - Side) similarity criterion for triangles states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle (the angle between the two sides) is equal, then the two triangles are similar. Let's analyze each option:

• Option 1: This describes the SSS (Side - Side - Side) similarity criterion, not SAS.
• Option 2: This describes the AA (Angle - Angle) similarity criterion, not SAS.
• Option 3: This correctly describes the SAS similarity criterion. It mentions two corresponding (proportional) sides and the included angle being equal (proven included angle measure) leading to triangle similarity.
• Option 4: This is about using a scale factor to determine similarity, which is a general concept related to similar figures but not the SAS criterion.

Answer:

The third option (the one with the text "If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.")