Question

1. use the figure shown, which statement must be true to prove ( j parallel k )? a. ( angle 2 cong angle 3 ) b. ( angle 1 cong angle 4 ) c. ( m angle 2 + m angle 5 = 180 ) d. ( angle 6 cong angle 4 )

Explanation:

Step1: Recall the converse of the alternate interior angles theorem

If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

Step2: Analyze each option

• Option A: $\angle2$ and $\angle3$ are vertical angles. Vertical angles are always congruent, but this does not prove $j\parallel k$.
• Option B: $\angle1$ and $\angle4$ are alternate exterior angles for lines $m$ and $n$ (not $j$ and $k$).
• Option C: $\angle2$ and $\angle5$ are not related in a way that would prove $j\parallel k$ by standard parallel line theorems.
• Option D: $\angle6$ and $\angle4$ are alternate interior angles. If $\angle6\cong\angle4$, then by the converse of the alternate interior angles theorem, $j\parallel k$.

Answer:

D. $\angle6\cong\angle4$