Question

Identify the postulate or theorem that would show that m || n (parallel lines).

Option 1: Alternate Exterior Angles Converse
Option 2: Alternate Interior Angles Converse
Option 3: Vertical Angles Converse
Option 4: Converse of the Corresponding Angles Postulate

Answer 1

The Converse of the Corresponding Angles Postulate is the correct choice to show that lines m and n are parallel, as it states that if corresponding angles are congruent, then the lines are parallel.

Step-by-step explanation:

To determine if lines m and n are parallel, you can use several postulates and theorems related to angles formed by two lines and a transversal. The correct choice in this case would be the Converse of the Corresponding Angles Postulate. This postulate states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Neither the Alternate Exterior Angles Converse nor the Alternate Interior Angles Converse explicitly talks about corresponding angles, which are required to use this postulate. The Vertical Angles Converse is not related to parallel lines, as vertical angles are the angles opposite each other when two lines intersect.