Question

determine whether each figure shows parallel lines. select yes or no for each figure.

Explanation:

Step1: Recall parallel - line property

Parallel lines have equal corresponding angles, alternate - interior angles, and same - side interior angles are supplementary.

Step2: Analyze first figure

The angles are \(85^{\circ}\) and \(95^{\circ}\). Since \(85^{\circ}+95^{\circ}=180^{\circ}\), these are same - side interior angles. But for parallel lines, same - side interior angles are supplementary when the lines are cut by a transversal. Here, the lines are not parallel. Answer: No.

Step3: Analyze second figure

The angles are both \(85^{\circ}\). These are corresponding angles. Since corresponding angles are equal, the lines are parallel. Answer: Yes.

Step4: Analyze third figure

The angles are \(85^{\circ}\) and \(95^{\circ}\). These are same - side interior angles. Since \(85^{\circ}+95^{\circ}=180^{\circ}\), the lines are parallel. Answer: Yes.

Step5: Analyze fourth figure

The angles are both \(95^{\circ}\). These are corresponding angles. Since corresponding angles are equal, the lines are parallel. Answer: Yes.

Answer:

1. No
2. Yes
3. Yes
4. Yes