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

Answer 1

The SAS (Side-Angle-Side) criterion can be used to prove the similarity of two triangles by verifying that two sides of one triangle are proportional to two sides of the other triangle, and that the included angles between those sides are congruent. In other words, if you have two triangles, and you can show that:

1. The lengths of two corresponding sides (let's call them \( a \) and \( b \) in one triangle, and \( c \) and \( d \) in the other) satisfy the proportionality condition \( \frac{a}{c} = \frac{b}{d} \).
2. The angle that is formed between those two sides in both triangles is the same (let's denote this angle as \( \angle A \) in the first triangle and \( \angle B \) in the second triangle, and \( \angle A = \angle B \)).

If both of these conditions are met, then the two triangles are similar by the SAS criterion.