Third Criterion for Similarity of Triangles: SSS Similarity
📐 What is Similarity?
Two triangles are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in the same ratio (proportional).
📖 SSS Similarity Criterion — Formal Definition
If the corresponding sides of two triangles are proportional (i.e., the ratios of all three pairs of corresponding sides are equal), then the two triangles are similar.
If in $\triangle ABC$ and $\triangle DEF$:
$$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$$
Then: $\triangle ABC \sim \triangle DEF$
⚠️ Key Point: The order of vertices matters! When we write $\triangle ABC \sim \triangle DEF$, it means:
- $A$ corresponds to $D$, $B$ corresponds to $E$, $C$ corresponds to $F$
- $\angle A = \angle D$, $\angle B = \angle E$, $\angle C = \angle F$