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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 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.

If all three side lengths are given and proportional to one another, resulting in the same scale factor, then the triangles are similar.

1 answer

The SAS (Side-Angle-Side) criterion for triangle similarity states that if two triangles have one angle that is equal and the lengths of the sides that are adjacent to that angle are in proportion (i.e., the ratios of the lengths of the corresponding sides are equal), then the two triangles are similar.

To use the SAS criterion to prove similarity in two triangles, follow these steps:

  1. Identify the Angle: Ensure that the angle between the two sides in question is known and that this angle is equal in both triangles.

  2. Check Side Proportions: Measure the lengths of the sides adjacent to the known angle in both triangles. The corresponding sides must have the same ratio (i.e., be proportional).

  3. Prove Similarity: If both conditions are satisfied (equal included angle and proportional sides), you can conclude that the two triangles are similar.

Thus, the correct response relating to the SAS criterion is: "If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar."