Question

consider the diagram.
diagram of two parallel lines p and q cut by a transversal r, with angles labeled 1,2,3,4 at the intersection of p and r, and 5,6,7,8 at the intersection of q and r
which theorem leads to the conclusion p || q if ∠1 ≅ ∠7?

• alternate interior angles converse theorem
• alternate exterior angles converse theorem
• same - side interior angles converse theorem
• same - side exterior angles converse theorem

Explanation:

To determine the theorem, we analyze the angles: $\angle 1$ and $\angle 7$ are alternate exterior angles (they lie outside the two lines \( p \) and \( q \) and on opposite sides of the transversal \( r \)). The Alternate Exterior Angles Converse Theorem states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel. Since $\angle 1 \cong \angle 7$, this theorem applies.

Answer:

B. Alternate Exterior Angles Converse Theorem