Question

Select the correct answer. Given: p || q, and r || s. Linear pair theorem that is angle 1 is supplementary to angle 2 moves down to angle 2 equals angle 6. As for parallel lines cut by a transversal, corresponding angles are congruent. This moves down to blank box with question mark. Prove: ∠1 and ∠14 are supplementary angles. Two vertical parallel lines p and q runs through two horizontal parallel lines r and s to form 16 angles numbered from 1 to 16. 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

Answer 1

The correct next step in the proof is A. Statement: ∠6 ≅ ∠14 Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

Since p || q and r || s, we know that angle 6 and angle 14 are corresponding angles. By the Corresponding Angles Theorem, we know that corresponding angles are congruent when parallel lines are cut by a transversal. Therefore, we can say that ∠6 ≅ ∠14.

To prove that ∠1 and ∠14 are supplementary angles, we can use the fact that ∠1 and ∠6 are a linear pair, which means that they are adjacent angles that form a straight line and are therefore supplementary. Since ∠6 ≅ ∠14, we can substitute ∠14 for ∠6 in the equation to get:

∠1 + ∠14 = 180°

Therefore, we have proved that ∠1 and ∠14 are supplementary angles.