Question

practice: proving parallel - numeric methods

1. determine which lines, if any, are parallel.
2. angle 4 and angle 2 each equal 72° and angles 9 and 14 each equal 108°

which of the following can be concluded from the diagram above?

Explanation:

Step1: Recall parallel - line angle rules

If corresponding angles are equal, or alternate - interior angles are equal, or same - side interior angles are supplementary, then the lines are parallel.

Step2: Analyze angles for lines a, b, c in the first diagram

For lines a, b, c, the angles formed by the transversal do not show equal corresponding, alternate - interior, or supplementary same - side interior angles. So, no lines among a, b, c are parallel.

Step3: Analyze angles in the second diagram

Angle 4 and angle 2 are equal (both 72°). They are corresponding angles. By the corresponding - angles postulate, if corresponding angles are equal, the lines are parallel. So, lines A and B are parallel. Also, angles 9 and 14 are supplementary (72° + 108°=180°). Since they are same - side interior angles and are supplementary, lines C and D are parallel.

Answer:

In the first diagram, no lines are parallel. In the second diagram, lines A and B are parallel, and lines C and D are parallel.