Final Answer:
The triangles are similar based on the Side-Angle-Side (SAS) criterion, where the corresponding sides AI/AM, IG/MN, and GF/NL are in proportion, and the included angles at I and M are congruent. The correct option is C) Yes; SAS; AIGF - AMNL.
Step-by-step explanation:
To determine if two triangles are similar, we can use the Side-Angle-Side (SAS) similarity criterion. In this case, the given triangles are AIGF and AMNL. The corresponding sides are AI and AM, IG and MN, and GF and NL. If the corresponding angles between these sides are congruent, the triangles are similar.
The statement "AA" stands for Angle-Angle, but the given triangles are not specified to have equal corresponding angles. Therefore, we rely on the SAS criterion. This means that the triangles share two pairs of proportional sides and have an included angle that is congruent. If the corresponding sides have a constant ratio, and the included angle is equal, the triangles are similar. The order of the corresponding sides and angles matters in a similarity statement.
In this case, option C correctly identifies the similarity as SAS, stating that AIGF is similar to AMNL. This indicates that the ratios of corresponding sides AI/AM, IG/MN, and GF/NL are equal, and the included angles at I and M are congruent. Therefore, option C is the correct choice for stating the reason and providing the similarity statement.