Question
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 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.
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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 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.
Skip to navigation
Answers
GPT-4o mini
The SAS (Side-Angle-Side) criterion can be used to prove the similarity of two triangles by checking the following condition:
**If two corresponding side lengths of each triangle are given and are proportional, along with a proven included angle measure, then the triangles are similar.**
This means that if you have two triangles, and you can show that:
1. The lengths of two sides of one triangle are proportional to the lengths of the corresponding sides of the other triangle (i.e., the ratio of the lengths of the two sides is the same).
2. The included angle (the angle between the two sides) between these sides in both triangles is equal.
Then, according to the SAS criterion, the two triangles are similar. This similarity implies that not only are their corresponding angles equal, but their corresponding sides are also in proportion to each other.
**If two corresponding side lengths of each triangle are given and are proportional, along with a proven included angle measure, then the triangles are similar.**
This means that if you have two triangles, and you can show that:
1. The lengths of two sides of one triangle are proportional to the lengths of the corresponding sides of the other triangle (i.e., the ratio of the lengths of the two sides is the same).
2. The included angle (the angle between the two sides) between these sides in both triangles is equal.
Then, according to the SAS criterion, the two triangles are similar. This similarity implies that not only are their corresponding angles equal, but their corresponding sides are also in proportion to each other.