Question

choose all of the following statements that prove that a and b are parallel. ∠3≅∠7 m∠4 + m∠6 = 180° ∠7≅∠8 ∠2≅∠6 ∠1≅∠2

Explanation:

Step1: Recall parallel - line postulates

Corresponding angles, alternate - interior angles, and same - side interior angles are related to parallel lines.

Step2: Analyze $\angle3\cong\angle7$

$\angle3$ and $\angle7$ are corresponding angles. If corresponding angles are congruent, then the lines are parallel.

Step3: Analyze $m\angle4 + m\angle6=180^{\circ}$

$\angle4$ and $\angle6$ are same - side interior angles. If same - side interior angles are supplementary, then the lines are parallel.

Step4: Analyze $\angle7\cong\angle8$

$\angle7$ and $\angle8$ are vertical angles. Vertical - angle congruence does not prove lines $A$ and $B$ are parallel.

Step5: Analyze $\angle2\cong\angle6$

$\angle2$ and $\angle6$ are corresponding angles. If corresponding angles are congruent, then the lines are parallel.

Step6: Analyze $\angle1\cong\angle2$

$\angle1$ and $\angle2$ are a linear pair. Their congruence (in the case of a $90^{\circ}$ linear pair) does not prove lines $A$ and $B$ are parallel.

Answer:

$\angle3\cong\angle7$, $m\angle4 + m\angle6 = 180^{\circ}$, $\angle2\cong\angle6$