Question

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

Explanation:

Step1: Analyze the proof - flow

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

Step2: Use parallel - line properties

Since we have parallel lines r || s, and ∠6 and ∠14 are corresponding angles for parallel lines r and s cut by a transversal.

Answer:

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