Question

1. lines a and b are cut by transversals c and d. if m(∠1)=m(∠3) and m(∠2)=m(∠4). can you conclude that a and b are parallel? explain your answer carefully.

Explanation:

Step1: Identify angle - type relationship

$\angle1$ and $\angle3$ are alternate - interior angles, $\angle2$ and $\angle4$ are also alternate - interior angles.

Step2: Apply parallel - line theorem

The converse of the alternate - interior angles theorem states that if two lines are cut by a transversal and the alternate - interior angles are congruent, then the two lines are parallel. Since $m(\angle1)=m(\angle3)$ and $m(\angle2)=m(\angle4)$, by the converse of the alternate - interior angles theorem, lines $a$ and $b$ are parallel.

Answer:

Yes, lines $a$ and $b$ are parallel.