Question

if ∠1≅∠2, can you conclude that any of the lines are parallel? explain. a. yes; lines n and p are parallel because corresponding angles are congruent. b. no; ∠1 and ∠2 show no relationship. c. yes; lines ℓ and m are parallel because corresponding angles are congruent. d. no; neither angle is formed by the transversal, line q.

Explanation:

Step1: Recall parallel - line postulate

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Step2: Identify the lines and angles

∠1 and ∠2 are corresponding angles formed when lines $\ell$ and $m$ are cut by a transversal. Since ∠1≅∠2, by the corresponding - angles postulate, lines $\ell$ and $m$ are parallel.

Answer:

C. Yes; lines $\ell$ and $m$ are parallel because corresponding angles are congruent.