Question

6 multiple choice 5 points
given the information in the diagram, which theorem best justifies why lines e and f must be parallel?
alternate interior angles theorem
consecutive (same-side) interior angles theorem
converse of the alternate interior angles theorem
converse of the consecutive (same-side) interior angles theorem

Explanation:

First, check the angles: $72^\circ + 108^\circ = 180^\circ$, so these are supplementary same-side interior angles. We are using the converse of a theorem (starting with angle relationships to prove lines parallel, not using parallel lines to prove angle relationships). The Converse of the Consecutive (Same-Side) Interior Angles Theorem states that if two same-side interior angles are supplementary, the lines cut by the transversal are parallel.

Answer:

D. Converse of the Consecutive (Same-Side) Interior Angles Theorem