Question

1. which of the following conditions is sufficient to prove lines are parallel?

adjacent angles are equal
adjacent angles are supplementary
vertical angles are congruent
alternate interior angles are congruent

Explanation:

Step1: Analyze adjacent angles

Adjacent angles being equal or supplementary does not necessarily prove lines are parallel. For example, in a non - parallel line intersection, adjacent angles can have various relationships.

Step2: Analyze vertical angles

Vertical angles are always congruent when two lines intersect, regardless of whether the lines are parallel or not. So this is not a sufficient condition for parallel lines.

Step3: Analyze alternate interior angles

By the Alternate Interior Angles Theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.

Answer:

Alternate Interior Angles are congruent