Question

given $\angle 10 \cong \angle 14$, which lines, if any, must be parallel based on the given information? justify your conclusion.\
\
$a \parallel b$, converse of the corresponding angles theorem\
$c \parallel d$, converse of the alternate exterior angles theorem\
$c \parallel d$, converse of the corresponding angles theorem\
not enough information to make a conclusion

Explanation:

Step1: Identify Angle Relationship

$\angle 10 \cong \angle 14$. Observe the lines: $\angle 10$ and $\angle 14$ are corresponding angles for lines $c$ and $d$ (cut by the transversal).

Step2: Apply Converse Theorem

The Converse of the Corresponding Angles Theorem states that if corresponding angles are congruent, then the lines are parallel. So, since $\angle 10 \cong \angle 14$ (corresponding angles), $c \parallel d$ by the Converse of the Corresponding Angles Theorem.

Answer:

c. $c \parallel d$, Converse of the Corresponding Angles Theorem