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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.

User Hitokiri
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2 Answers

11 votes

Answer:

The next logical step in the proof is to apply the Corresponding Angles Converse Postulate, stating that if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Step-by-step explanation:

Given that \( p \parallel q \) and \( r \parallel s \), we have corresponding angles that are congruent. Specifically, angle \( 1 \) corresponds to angle \( 14 \) because both are formed by the intersection of \( p \) and \( r \).

According to the Corresponding Angles Converse Postulate, if corresponding angles are congruent, then the lines are parallel.

Therefore, we can conclude that \( p \parallel r \). Since \( p \) is parallel to \( r \) and \( r \) is parallel to \( s \), by the Transitive Property of Parallel Lines, \( p \parallel s \).

Now, since \( p \parallel s \), angle \( 1 \) and angle \( 14 \) are corresponding angles of the parallel lines \( p \) and \( s \). Hence, angle \( 1 \) is congruent to angle \( 14 \).

We know that supplementary angles have a sum of \( 180^\circ \), so if angle \( 1 \) is congruent to angle \( 14 \), then angles \( 1 \) and \( 14 \) are supplementary.

Therefore, the next step is to explicitly state and use the Corresponding Angles Converse Postulate to establish that \( p \parallel s \), and then conclude that \( \angle 1 \) and \( \angle 14 \) are supplementary angles.

User Ravikt
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5 votes

Answer:

Step-by-step explanation:

the answer is D

User Evpo
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