Question

in the figure below, it is given that \\( \angle 4 \cong \angle 6 \\).
which property could be used to prove that \\( p \parallel q \\) in the fewest number of steps?
if consecutive interior angles are supplementary, then the lines are parallel.
if alternate exterior angles are congruent, then the lines are parallel.
if alternate interior angles are congruent, then the lines are parallel.
if corresponding angles are congruent, then the lines are parallel.

Explanation:

Step1: Analyze the position of ∠4 and ∠6

∠4 and ∠6 are alternate interior angles.

Step2: Recall the parallel - line theorems

The theorem “If alternate interior angles are congruent, then the lines are parallel” directly applies here as we are given ∠4 ≅ ∠6.

Answer:

If alternate interior angles are congruent, then the lines are parallel.