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 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.
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 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.
Answers
GPT-4o mini
The SAS (Side-Angle-Side) criterion for triangle similarity states that if two triangles have two pairs of corresponding sides that are proportional and the included angle between those sides is equal, then the triangles are similar.
In other words, for triangles ABC and DEF, if the following conditions are met:
1. \( \frac{AB}{DE} = \frac{AC}{DF} \) (the lengths of two corresponding sides are in proportion)
2. \( \angle A = \angle D \) (the included angle is equal)
then triangle ABC is similar to triangle DEF, which can be denoted as \( \triangle ABC \sim \triangle DEF \).
Thus, the correct response for using the SAS criterion to prove similarity in triangles is:
"If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar."
In other words, for triangles ABC and DEF, if the following conditions are met:
1. \( \frac{AB}{DE} = \frac{AC}{DF} \) (the lengths of two corresponding sides are in proportion)
2. \( \angle A = \angle D \) (the included angle is equal)
then triangle ABC is similar to triangle DEF, which can be denoted as \( \triangle ABC \sim \triangle DEF \).
Thus, the correct response for using the SAS criterion to prove similarity in triangles is:
"If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar."