Question

problem 11: (first taught in lesson 24) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: ℓ || m prove: ∠3 and ∠6 are supplementary. diagram with lines ℓ, m, n and angles 1,2,3,4 (on ℓ) and 5,6,7,8 (on m), cut by transversal n a b c d e a if two parallel lines are cut by a transversal, then corresponding angles are supplementary.

Explanation:

1. Given \( \ell \parallel m \) and transversal \( n \).
2. \( \angle 3 \) and \( \angle 6 \) are same - side interior angles (or can be related via corresponding angles logic when considering parallel lines cut by transversal). The property that when two parallel lines are cut by a transversal, corresponding (or same - side interior in this context - related) angles have supplementary relationship justifies that \( \angle 3 \) and \( \angle 6 \) are supplementary. The option A states the relevant property about parallel lines and transversal leading to supplementary angles for corresponding (or related) angles.

Answer:

A. If two parallel lines are cut by a transversal, then corresponding angles are supplementary.