Same-Side Interior Angles Postulate
The image shows two lines crossed by a transversal, with angles labeled ∠1 and ∠2. We are given that the measures of ∠1 and ∠2 sum to 180°.
If two angles sum to 180 degrees and are on the same side of a transversal, they are known as consecutive interior angles or same-side interior angles. According to the Same-Side Interior Angles Postulate, if two angles on the same side of a transversal are supplementary (sum to 180 degrees), then the lines that are intersected by the transversal are parallel.
Given that the measure of angle 1 (m∠1) plus the measure of angle 2 (m∠2) equals 180 degrees, this satisfies the condition for the Same-Side Interior Angles Postulate. Therefore, the lines g and h are parallel based on this postulate.
The correct answer to the question, "Which lines are parallel if m∠1 + m∠2 = 180°?", with the justification answer is:
∠ g || ∠ h, by the Converse of the Same-Side Interior Angles Postulate
This corresponds to the first choice in the multiple-choice options provided in the image.
