The correct answer is c: "If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar."
Explanation:
The SAS (Side-Angle-Side) criterion for triangle similarity states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between those sides is the same, then the two triangles are similar. This means that their corresponding angles are also equal, and their corresponding sides are in proportion.
- Option a refers to the SSS (Side-Side-Side) criterion, which states that if all three sides of one triangle are proportional to all three sides of another triangle, then the triangles are similar.
- Option b refers to the AA (Angle-Angle) criterion, which states that if two angles in one triangle are equal to two angles in another triangle, then the triangles are similar.
- Option d mentions having a scale factor but does not directly convey the requirements of the SAS criterion for similarity.
Therefore, option c specifically describes the conditions necessary for applying the SAS criterion to establish that the two triangles are similar.
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