Question

in this figure, lines a and b are intersected by line t. which of these statements proves that lines a and b are parallel? ∠1=∠3 ∠1 and ∠3 are complementary. ∠1=∠2 ∠1 and ∠2 are

Explanation:

Step1: Recall parallel - line postulates

If two lines are cut by a transversal, corresponding angles being equal proves the lines are parallel. $\angle1$ and $\angle3$ are corresponding angles.

Step2: Analyze each option

• If $\angle1=\angle3$, by the corresponding - angles postulate, lines $a$ and $b$ are parallel.
• If $\angle1$ and $\angle3$ are complementary, it does not prove the lines are parallel.
• $\angle1$ and $\angle2$ are a linear pair, and their equality ($\angle1 = \angle2$) means they are right - angles, but this does not prove $a$ and $b$ are parallel.

Answer:

$\angle1=\angle3$