Question

which statement must be true to prove l || k? a. ∠2≅∠3 b. ∠1≅∠4 c. m∠2 + m∠5 = 180 d. ∠6≅∠4

Explanation:

Step1: Recall parallel - line postulates

When two lines are cut by a transversal, certain angle - relationships prove parallel lines.

Step2: Analyze option A

$\angle2$ and $\angle3$ are vertical angles. Vertical angles are always congruent, but their congruence does not prove $j\parallel k$.

Step3: Analyze option B

$\angle1$ and $\angle4$ are vertical angles. Their congruence does not prove $j\parallel k$.

Step4: Analyze option C

$\angle2$ and $\angle5$ are not corresponding, alternate - interior, or alternate - exterior angles. Their sum being 180 degrees does not prove $j\parallel k$.

Step5: Analyze option D

$\angle6$ and $\angle4$ are alternate - interior angles. If alternate - interior angles are congruent when two lines are cut by a transversal, then the two lines are parallel. So, if $\angle6\cong\angle4$, then $j\parallel k$.

Answer:

D. $\angle6\cong\angle4$