Question

If x=y, the reason why lines p and q are parallel is:

a) Not enough information is provided
b) Transitive property of parallel lines
c) Alternate exterior angles converse theorem
d) Corresponding angles converse theorem

Answer 1

The reason why lines p and q are parallel when x=y is the Alternate Exterior Angles Converse Theorem.

Step-by-step explanation:

The correct answer is c) Alternate exterior angles converse theorem.

When it is given that x=y, it implies that the lines p and q are parallel. The theorem that establishes this relationship is the Alternate Exterior Angles Converse Theorem. According to this theorem, if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.