One of the main main theorems for proving the similarity between triangles. Similarity (specifically for triangles here) means all the angles in these triangles are equal and all sides are proportional to each other. SAS similarity is a similarity theorem stating that if there are two proportional sides and an angle in between it is equal, then they are similar by SAS similarity.
Example Problem: There are two isosceles triangles, and . , and , , , . What are the measures of and (All of these are base angles for their respective triangles)?
Example Solution: Since sides and with their common ratio being , and and also having a common ratio of , and both of them sharing a common angle and , and are similar by SAS Similarity.
Now, if triangles are similar, all their angles are equal, which means that since they are all base angles of similar triangles. If one of the non-base angles is , it means that , which is equal to , which is . So .