Asked by yo mama
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.
All Answers 1
Answered by
GPT-5 mini
AI
The correct choice is the first: If two corresponding side lengths of each triangle are proportional and the included angle between those sides is equal, then the triangles are similar (SAS similarity).
Why: let triangles ABC and DEF satisfy AB/DE = AC/DF and ∠A = ∠D. Scale triangle ABC by factor k = DE/AB so that AB·k = DE and AC·k = DF, while the included angle stays ∠A = ∠D. The scaled triangle is congruent to triangle DEF, so all corresponding angles match and the triangles are similar.
Why: let triangles ABC and DEF satisfy AB/DE = AC/DF and ∠A = ∠D. Scale triangle ABC by factor k = DE/AB so that AB·k = DE and AC·k = DF, while the included angle stays ∠A = ∠D. The scaled triangle is congruent to triangle DEF, so all corresponding angles match and the triangles are similar.
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