Question

choose all of the following statements that prove that y and z are parallel.

Explanation:

Step1: Recall parallel - line postulates and theorems

When two lines are cut by a transversal, certain angle - relationships prove parallel lines. Corresponding angles being congruent, alternate interior angles being congruent, and same - side interior angles being supplementary prove two lines are parallel.

Step2: Analyze $\angle3\cong\angle7$

$\angle3$ and $\angle7$ are corresponding angles. If corresponding angles are congruent, then the two lines ($Y$ and $Z$) are parallel.

Step3: Analyze $\angle6\cong\angle7$

$\angle6$ and $\angle7$ are vertical angles. Vertical - angle congruence does not prove that $Y$ and $Z$ are parallel.

Step4: Analyze $\angle2\cong\angle6$

$\angle2$ and $\angle6$ are corresponding angles. If corresponding angles are congruent, then the two lines ($Y$ and $Z$) are parallel.

Step5: Analyze $m\angle3 + m\angle5=180^{\circ}$

$\angle3$ and $\angle5$ are same - side interior angles. If same - side interior angles are supplementary (sum to $180^{\circ}$), then the two lines ($Y$ and $Z$) are parallel.

Step6: Analyze $\angle3\cong\angle5$

$\angle3$ and $\angle5$ are alternate interior angles. If alternate interior angles are congruent, then the two lines ($Y$ and $Z$) are parallel.

Answer:

$\angle3\cong\angle7$, $\angle2\cong\angle6$, $m\angle3 + m\angle5 = 180^{\circ}$, $\angle3\cong\angle5$