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 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.
If at least two angles of the triangles are given and are the same, 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 correct response:
"If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar."

Brief justification:
Let the two pairs of corresponding sides be in the ratio k. Multiply (scale) one triangle by k so its two corresponding sides become equal to the other triangle's two sides; the included angle stays the same. With two sides and the included angle equal, the scaled triangle and the other triangle are congruent (SAS congruence), so all corresponding angles match. Therefore the original triangles are similar (corresponding sides are proportional and corresponding angles equal).