Second Criterion for Similarity of Triangles (SAS Similarity)
📐 What is Similarity?
Two triangles are similar if they have the same shape but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are in proportion (have the same ratio).
🔑 SAS Similarity Criterion — The Statement
SAS Similarity Theorem: If one angle of a triangle is equal to one angle of another triangle, and the sides including these angles are in the same ratio (proportional), then the two triangles are similar.
Formally, in $\triangle ABC$ and $\triangle DEF$:
If $\angle A = \angle D$ and $\dfrac{AB}{DE} = \dfrac{AC}{DF}$, then $\triangle ABC \sim \triangle DEF$
Key Point: The equal angle must be the included angle — the angle formed between the two proportional sides.