QuestionWhich statement is true for triangles $A B C$ and $D E F$ with $A B=9, B C=15, D E=6, E F=10$, and $\angle B \cong \angle E$? a. $\angle C A B \cong \angle D E F$ b. $\frac{A B}{C B}=\frac{F E}{D E}$ c. $\triangle A B C \cong \triangle D E F$ d. $\frac{A B}{D E}=\frac{F E}{C B}$

Studdy Solution
Now, let's check each statement given in the problem to see which one is true.
a. $\angle CAB \cong \angle DEF$
We don't have enough information to determine whether this statement is true, so we can't choose this option.
b. $\frac{AB}{CB} = \frac{FE}{DE}$This is not the correct ratio of the corresponding sides of the similar triangles, so this statement is false.
c. $\triangle ABC \cong \triangle DEF$
The triangles are similar, not congruent, so this statement is false.
d. $\frac{AB}{DE} = \frac{FE}{CB}$This is the correct ratio of the corresponding sides of the similar triangles, so this statement is true.
The correct answer is d. $\frac{AB}{DE} = \frac{FE}{CB}$.