Question

Given: m || n, ∠1 ≅ ∠3. Prove: p || q. Horizontal parallel lines n and m are cut by transversals q and p. At the intersection of lines q and m, the uppercase right angle is angle 3. At the intersection of lines p and m, the uppercase right angle is angle 2. At the intersection of lines p and n, the bottom left angle is angle 1. Complete the two-column proof. ™£ = Line p parallel to line q ™¦ = Transitive property ™ = Converse corresponding angles theorem.

Answer 1

To prove that p is parallel to q, we can use the properties of parallel lines. Given that m is parallel to n and angle 1 is congruent to angle 3, we can use the Converse Corresponding Angles Theorem to show that p and q are parallel.

Step-by-step explanation:

To prove that p is parallel to q, we need to use the properties of parallel lines and corresponding angles. We are given that m is parallel to n, and that angle 1 is congruent to angle 3. From the Converse Corresponding Angles Theorem, we know that if angle 1 is congruent to angle 3, then lines p and q must be parallel. Therefore, we can conclude that p || q.