Question

from the diagram below, select the pair of lines that must be parallel for each statement below to be true. if there is no pair of lines, select “none.” (d)17. ∠2≅∠5 a. o||q b. ℓ||m c. p||q d. o||p e. none 18. ∠3 and ∠5 are supplementary. a. ℓ||m b. o||p c. p||q d. ℓ||n e. none 19. ∠3≅∠4 a. o||p b. m||n c. o||q d. ℓ||n e. none

Explanation:

Step1: Recall corresponding - angles postulate

If two parallel lines are cut by a transversal, corresponding angles are congruent. $\angle2$ and $\angle5$ are corresponding angles when lines $o$ and $p$ are cut by transversal $\ell$. So, when $o\parallel p$, $\angle2\cong\angle5$.

Step2: Recall same - side interior angles theorem

If two parallel lines are cut by a transversal, same - side interior angles are supplementary. $\angle3$ and $\angle5$ are same - side interior angles when lines $\ell$ and $m$ are cut by transversal $p$. So, when $\ell\parallel m$, $\angle3$ and $\angle5$ are supplementary.

Step3: Recall alternate interior angles theorem

If two parallel lines are cut by a transversal, alternate interior angles are congruent. $\angle3$ and $\angle4$ are alternate interior angles when lines $m$ and $n$ are cut by transversal $p$. So, when $m\parallel n$, $\angle3\cong\angle4$.

Answer:

1. D. $o\parallel p$
2. A. $\ell\parallel m$
3. B. $m\parallel n$