Question

given $\angle 11 \cong \angle 13$.
which lines, if any, must be parallel based on the
given information? justify your conclusion.

\bigcirc $c \parallel d$, converse of the alternate exterior angles theorem
\bigcirc $a \parallel b$, converse of the corresponding angles theorem
\bigcirc $c \parallel d$, converse of the same - side interior angles theorem
\bigcirc not enough information to make a conclusion

Explanation:

1. Identify the angles: \( \angle 11 \) and \( \angle 13 \) are alternate exterior angles formed by transversal \( a \) intersecting lines \( c \) and \( d \).
2. Apply the theorem: The Converse of the Alternate Exterior Angles Theorem states that if alternate exterior angles are congruent, then the lines cut by the transversal are parallel. Since \( \angle 11 \cong \angle 13 \), by this converse theorem, \( c \parallel d \).

Answer:

A. \( c \parallel d \), Converse of the Alternate Exterior Angles Theorem