Geometry: Common Core (15th Edition)

$\frac{AB}{DB} = \frac{BC}{BF}$
We are given that $\triangle ABC$ ∼ $\triangle DBF$. In similar triangles, corresponding angles are congruent and corresponding sides are proportional. Let us list the corresponding sides in the two triangles: $AB ≅ DB$ $BC ≅ BF$ $CA ≅ FD$ The scale factor is the same for each set of corresponding sides. A proportion can be written that compares corresponding sides of the two triangles: $\frac{AB}{DB} = \frac{BC}{BF}$