Question

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

Explanation:

Step1: Identify Angle Relationship

Given \( \angle 10 \cong \angle 14 \). Observe the lines and transversal: \( \angle 10 \) and \( \angle 14 \) are alternate exterior angles for lines \( c \) and \( d \) with the transversal (the slanted line).

Step2: Apply Converse Theorem

The Converse of the Alternate Exterior Angles Theorem states that if alternate exterior angles are congruent, then the lines are parallel. Since \( \angle 10 \cong \angle 14 \) (alternate exterior angles), by the Converse of Alternate Exterior Angles Theorem, \( c \parallel d \).

Answer:

\( c \parallel d \), Converse of the Alternate Exterior Angles Theorem (the third option: \( c \parallel d \), Converse of the Alternate Exterior Angles Theorem)