Final answer:
To prove triangles are similar by SAS~, demonstrate two pairs of sides are in proportion and the included angles are equal, using proportions or trigonometry if necessary.
Step-by-step explanation:
To prove that triangles are similar by the SAS~ (Side-Angle-Side Similarity) criterion, you need to show that two sides of one triangle are in proportion to two corresponding sides of the other triangle, and the included angles are equal.
For instance, if you have triangles ∆ABC and ∆DEF, you would need to prove something like AB/DE = BC/EF, along with a statement that angle B is equal to angle E. If one value is missing for the similarity, you must find it by using relevant proportions or by calculating angles using trigonometric identities or the Law of Sines or Law of Cosines based on the information provided.