Question

definition of similar figures quick check
explain how the sas criterion can be used to prove similarity in two triangles. (1 point)

if given a scale factor, you can determine if 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 at least two angles of the triangles are given and are the same, 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.

Explanation:

The SAS (Side - Angle - Side) similarity criterion for triangles states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle (the angle between the two sides) is congruent, then the two triangles are similar.

• The first option is incorrect because a scale factor alone doesn't directly relate to the SAS criterion.
• The third option describes the AA (Angle - Angle) similarity criterion, not SAS.
• The fourth option describes the SSS (Side - Side - Side) similarity criterion, not SAS.
• The second option correctly states the requirements of the SAS similarity criterion: two proportional corresponding sides and a proven (congruent) included angle.

Answer:

B. If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.