Question

choose all of the following statements that prove that a and b are parallel. ∠1≅∠2 ∠3≅∠6 ∠6≅∠7 m∠5 + m∠6 = 180° m∠4 + m∠6 = 90°

Explanation:

Step1: Recall parallel - line postulates

Corresponding angles, alternate - interior angles being congruent and same - side interior angles being supplementary prove lines are parallel.

Step2: Analyze $\angle1\cong\angle2$

$\angle1$ and $\angle2$ are vertical angles, not related to parallel - line postulates.

Step3: Analyze $\angle3\cong\angle6$

$\angle3$ and $\angle6$ are alternate - interior angles. If alternate - interior angles are congruent, then lines $A$ and $B$ are parallel.

Step4: Analyze $\angle6\cong\angle7$

$\angle6$ and $\angle7$ are vertical angles, not related to parallel - line postulates.

Step5: Analyze $m\angle5 + m\angle6=180^{\circ}$

$\angle5$ and $\angle6$ are not same - side interior angles for lines $A$ and $B$.

Step6: Analyze $m\angle4 + m\angle6 = 90^{\circ}$

This angle - sum relationship is not related to parallel - line postulates.

Answer:

$\angle3\cong\angle6$