New Criteria for Triangle Similarity
Stephen Yang · Mathematics Magazine · 2025
SummaryWe propose and prove two new criteria for triangle similarity. We name these, in conjunction, the SS-AA similarity criteria. These criteria are unique in that they utilize ratios between angles as conditions, which are rarely used, and similarity is not immediately apparent. Generally, if the ratios of a corresponding pair of sides are equal and the ratios of a corresponding pair of angles are equal, then the two triangles are similar. The sole exception is explained in the body of the article.