Conditions for Similar Triangles

Condition: $\angle A=\angle P$, $\angle B=\angle Q$ and $\angle C=\angle R$

Result: $\Delta ABC \sim \Delta PQR$

Reference: A.A.A.

Condition: $\dfrac{AB}{PQ}=\dfrac{BC}{QR}=\dfrac{AC}{PR}$

Result: $\Delta ABC \sim \Delta PQR$

Reference: 3 sides in prop.

Condition: $\dfrac{AB}{PQ}=\dfrac{BC}{QR}$ and $\angle B = \angle Q$

Result: $\Delta ABC \sim \Delta PQR$

Reference: ratio of 2 sides, inc. $\angle$