Question

which of the following does not always prove lines are parallel?
a congruent alternate interior angles
c congruent vertical angles
b congruent alternate exterior angles
d congruent corresponding angles

Explanation:

• Congruent alternate interior angles: By the Alternate Interior Angles Theorem, if alternate interior angles are congruent, then the lines are parallel.
• Congruent alternate exterior angles: By the Alternate Exterior Angles Theorem, if alternate exterior angles are congruent, then the lines are parallel.
• Congruent vertical angles: Vertical angles are always congruent, but they do not necessarily imply that the lines are parallel. Vertical angles are formed by two intersecting lines, and their congruence is a property of intersecting lines, not parallel lines.
• Congruent corresponding angles: By the Corresponding Angles Theorem, if corresponding angles are congruent, then the lines are parallel.

Answer:

C. Congruent vertical angles