Question

based on this information, what conjecture can be made about the geometric relationship shown lines and angles?
a if two lines are parallel and cut by a transversal, then same side interior angles are co
b if two lines are parallel and cut by a transversal, then alternate exterior angles are co
c vertical angles are congruent if and only if lines are parallel.
d adjacent angles are congruent if and only if lines are parallel.

Explanation:

• Option A: When two parallel lines are cut by a transversal, same - side interior angles are supplementary. This is a well - known property in geometry related to parallel lines and transversals.
• Option B: When two parallel lines are cut by a transversal, alternate exterior angles are congruent, not supplementary.
• Option C: Vertical angles are always congruent, regardless of whether the lines are parallel or not.
• Option D: Adjacent angles are not necessarily congruent just because lines are parallel. Adjacent angles formed by intersecting lines (even non - parallel) have a common side and vertex, but their measures are related in different ways (e.g., adjacent angles on a straight line are supplementary).

Answer:

A. If two lines are parallel and cut by a transversal, then same side interior angles are co