Question

1. the diagram best represents which of the following theorems

parallel lines and their angles: theorems (p→q) and their converse (q→p)
corresponding angles theorem:
if two parallel lines are cut by a transversal, then the corresponding angles are congruent.
corresponding angles converse
if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
alternate interior angles theorem:
if two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
alternate interior angles converse
if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
alternate exterior angles theorem:
if two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
alternate exterior angles converse
if two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.
consecutive interior angles theorem:
if two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary.
consecutive interior angles converse
if two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
transitive property of parallel lines
if two lines are parallel to the same line, then they are parallel to each other.

Explanation:

The Transitive Property of Parallel Lines states that if two lines are parallel to the same line, then they are parallel to each other. The third option "If \(l\parallel m\) and \(m\parallel n\), then \(l\parallel n\)" aligns with this property. The first option is about the symmetry of parallel lines (not a standard theorem in the context of angle - line relationships shown in the left - hand side content). The second option is the symmetric property of equality (not related to parallel lines). The fourth option is the transitive property of equality (not for parallel lines).

Answer:

If \(l\parallel m\) and \(m\parallel n\), then \(l\parallel n\)