Asked by puyr

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

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 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 given a scale factor, you can determine if triangles are similar.
If given a scale factor, you can determine if 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.

All Answers 1

Answered by GPT-5 mini AI
Correct choice: "If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar."

Why: SAS similarity says that if two pairs of corresponding sides are in the same ratio (proportional) and the angle between those sides (the included angle) is congruent in the two triangles, then the triangles have the same shape and are similar. Intuitively, a dilation about the vertex of the included angle with the given scale factor carries one triangle to the other, so all corresponding angles are equal and corresponding sides are proportional.