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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 given a scale factor, you can determine if triangles are similar.
If given a scale factor, you can determine if 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 two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.

1 answer

The SAS (Side-Angle-Side) criterion states that if two triangles have one angle that is equal and the lengths of the sides that form that angle are in proportion, then the triangles are similar.

In other words, to use the SAS criterion for proving similarity, you would follow these steps:

  1. Identify two corresponding sides in the two triangles.
  2. Confirm that these sides are proportional, meaning the ratio of the lengths of the two sides in one triangle is equal to the ratio of the lengths of the two corresponding sides in the other triangle.
  3. Ensure that the included angle (the angle between the two sides you are considering) in both triangles is equal.

If both conditions are met—the corresponding sides are proportional and the included angles are equal—then you can conclude that the two triangles are similar by the SAS criterion.