Question Explain how the SAS criterion can be used to prove similarity in two triangles.(1 point) Responses If at least two angles of the triangles are given and are the same, 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 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. If given a scale factor, you can determine if triangles are similar. If all three side lengths are given and proportional to one another, resulting in the same scale factor, then the triangles are similar. If all three side lengths are given and proportional to one another, resulting in the same scale factor, then the triangles are similar.

Answer 1

The SAS (Side-Angle-Side) criterion is a method used to prove the similarity of two triangles. According to the SAS criterion, if two sides of one triangle are proportional to two sides of another triangle, and the included angle between those two sides is congruent to the included angle of the other triangle, then the two triangles are similar.

To summarize:

• Proportional Sides: If \( \frac{AB}{DE} = \frac{AC}{DF} \) (where \( AB \) and \( AC \) are sides of Triangle 1, and \( DE \) and \( DF \) are sides of Triangle 2).

• Congruent Included Angle: If the angle between those two sides in Triangle 1 (let’s call it \( \angle A \)) is congruent to the angle between the two corresponding sides in Triangle 2 (let’s call it \( \angle D \)).

Thus, if both conditions are met, you can conclude that the two triangles are similar by the SAS criterion.