Question

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

Explanation:

Step1: Recall parallel - line postulates

If two lines are cut by a transversal, certain angle - relationships prove parallelism.

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 same - side interior angles. If the sum of same - side interior angles is $180^{\circ}$, then the two lines ($j$ and $k$) are parallel.

Step5: Analyze option D

$\angle6$ and $\angle4$ are not corresponding, alternate interior, or same - side interior angles. Their congruence does not prove $j\parallel k$.

Answer:

C. $m\angle2 + m\angle5=180$