## Geometry: Common Core (15th Edition)

Yes, the triangles would be similar because two sides in one triangle are proportional to two sides in the other triangle, and the included angle in both triangles are congruent because they are vertical angles (vertical angles are congruent). Thus, $\triangle ABE$ ~ $\triangle CBD$ using the SAS Similarity Theorem. $x = \frac{25}{3}$
Let's set up the proportion of corresponding sides in $\triangle ABE$ and $\triangle CBD$: $\frac{AB}{CB} = \frac{EB}{DB}$ Let's plug in what we are given: $\frac{6}{10} = \frac{5}{x}$ Use the cross products property to eliminate the fractions: $6x = 50$ Divide both sides by $6$ to solve for $x$: $x = \frac{50}{6}$ Divide both the numerator and denominator by their greatest common factor, $2$: $x = \frac{25}{3}$