Question

explain how you could use the sas criterion to determine that the triangles are similar. (1 point) reflect the triangle across the y - axis and check for symmetry. use translation by sliding triangle ( abc ) to a corresponding angle in triangle ( abc ) and check for similarity. determine the two side lengths on either side of the shared ordered pair at point ( a ) for both triangles and then compare for proportionality. find the scale factor by comparing angles of each triangle and check for proportionality.

Explanation:

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

• Option 1: Reflecting across the y - axis and checking for symmetry is related to congruence (or symmetry) rather than the SAS similarity criterion for triangles.
• Option 2: Translation and checking for similarity in this way does not directly relate to the SAS criterion which is about proportional sides and included angles.
• Option 3: To use SAS, we need to look at two sides and the included angle. If we determine the two side lengths on either side of the shared ordered pair (which would be the included angle at point A) for both triangles and then check if these sides are proportional, this is in line with the SAS similarity criterion.
• Option 4: Finding the scale factor by comparing angles is not the SAS criterion (SAS is about sides and included angle, not just comparing angles to find scale factor).

Answer:

C. Determine the two side lengths on either side of the shared ordered pair at point \( A \) for both triangles and then compare for proportionality.