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

Question

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

Responses

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 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.

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 at least two angles of the triangles are given and are the same, then the triangles are similar

Answer 1

Bot GPT 4-o mini answered
2 hours ago

The SAS (Side-Angle-Side) criterion can be used to prove the similarity of two triangles by the following statement:

If two corresponding side lengths of each triangle are proportional, and the included angle between those sides is equal, then the two triangles are similar.

This means that if you have two pairs of sides from each triangle that are in proportion (for example, if side AB of triangle ABC is proportional to side DE of triangle DEF, and side AC is proportional to side DF), and the angle formed between those two sides in both triangles is the same (angle A in triangle ABC is equal to angle D in triangle DEF), then you can conclude that the two triangles are similar.

Thus, the first response option you provided succinctly captures this concept:

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