Final answer:
When two triangles are proven similar through the SAS (Side-Angle-Side) similarity criterion, it means that one triangle has two sides that are proportional in length to two corresponding sides of the other triangle, and the included angles are congruent in both triangles.
Step-by-step explanation:
When two triangles are proven similar through the SAS (Side-Angle-Side) similarity criterion, it means that one triangle has two sides that are proportional in length to two corresponding sides of the other triangle, and the included angles are congruent in both triangles.
For example, if triangle ABC and triangle DEF have the following properties:
- AB/DE = BC/EF (the ratio of the lengths of corresponding sides is equal)
- Angle B = Angle E (the included angles are congruent)
- AC/DF or CA/EF (the ratio of their remaining sides is mutually proportional or not)
Then, we can prove that triangles ABC and DEF are similar through the SAS similarity criterion.