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: Identify angle - type relationship

$\angle1$ and $\angle2$ are corresponding angles formed by lines $\ell$ and $m$ with a transversal.

Step2: Apply parallel - line theorem

If corresponding angles are congruent, then the lines are parallel. Since $\angle1=\angle2$, lines $\ell$ and $m$ are parallel.

Answer:

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