Question

for use with pages 150 - 156
is it possible to prove that lines p and q are parallel? if so, explain how.
1.
2.

Explanation:

Step1: Recall parallel - line angle relationships

If two lines are cut by a transversal, and the same - side interior angles are supplementary (sum to 180°), the lines are parallel. Also, if corresponding angles are equal, the lines are parallel.

Step2: Analyze the first pair of lines

For lines \(p\) and \(q\) in the first figure, the 124° angle and the 56° angle are same - side interior angles. Calculate their sum: \(124 + 56=180\). Since the sum of the same - side interior angles is 180°, lines \(p\) and \(q\) are parallel.

Step3: Analyze the second pair of lines

For lines \(p\) and \(q\) in the second figure, consider the angles formed by the transversal. The angles given do not satisfy any of the parallel - line angle relationships. For example, if we consider the 58° and 74° angles with respect to line \(p\) and the 132° angle with respect to line \(q\), there is no pair of corresponding, alternate interior, or same - side interior angles that satisfy the parallel - line conditions. The sum of the angles formed on the same side of the transversal does not equal 180°. So, lines \(p\) and \(q\) are not parallel.

Answer:

1. Yes, because the same - side interior angles (124° and 56°) are supplementary.
2. No, because the angle measures do not satisfy the parallel - line angle relationships.