Question

use the figure shown. 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 the transversal $q$.

Step2: Apply parallel - line theorem

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

Answer:

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