Question

question 1 not yet answered marked out of 2.00 flag question in which diagrams are two lines parallel? 1. 2. 3. select one: a. choice 2 and choice 3 b. choices 1, 2, and 3 c. choice 1 only d. choice 1 and choice 3

Explanation:

Step1: Recall parallel - line criteria

If two lines are cut by a transversal, then the lines are parallel if corresponding angles are equal, alternate - interior angles are equal, or same - side interior angles are supplementary.

Step2: Analyze Diagram 1

In Diagram 1, the two angles given ($109^{\circ}$ and $108^{\circ}$) are neither equal nor supplementary. So the lines are not parallel.

Step3: Analyze Diagram 2

In Diagram 2, $58^{\circ}+122^{\circ}=180^{\circ}$. The two angles are same - side interior angles and they are supplementary. So the lines are parallel.

Step4: Analyze Diagram 3

In Diagram 3, the two $67^{\circ}$ angles are corresponding angles. Since corresponding angles are equal, the lines are parallel.

Answer:

a. Choice 2 and Choice 3