Question

given: p || q, and r || s. prove: ∠1 and ∠14 are supplementary angles. ∠1 is supplementary to ∠2. linear pair theorem ∠2 = ∠6. for parallel lines cut by a transversal, corresponding angles are congruent. what is the next step in the proof? choose the most logical approach. a. statement: ∠6 ≅ ∠14 reason: for parallel lines cut by a transversal, corresponding angles are congruent b. statement: ∠6 ≅ ∠7 reason: vertical angles theorem c. statement: ∠6 and ∠5 are supplementary reason: linear pair theorem d. statement: m∠6 + m∠8 = 180° reason: angle addition

Explanation:

Step1: Analyze the given proof steps

We know that ∠1 is supplementary to ∠2 (Linear - Pair Theorem) and ∠2 = ∠6 (corresponding angles for parallel lines). To prove that ∠1 and ∠14 are supplementary, we need to connect ∠6 and ∠14.

Step2: Recall angle - relationships in parallel lines

When parallel lines are cut by a transversal, corresponding angles are congruent. Since we want to get from ∠6 to ∠14, and they are corresponding angles for parallel lines, we can use the property of corresponding angles for parallel lines.

Answer:

A. Statement: ∠6≅∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent