Question

1. determine which lines, if any, are parallel.
2. line m is a transversal. for lines a, b, c, and d; determine which line is not parallel to the others.

21.

Explanation:

Step1: Recall parallel - line angle rules

If two lines are parallel and a transversal intersects them, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Analyze angles for each option in problem 17

For lines \(d\) and \(e\) in problem 17, we can see that the corresponding angles formed by the transversals are equal. For example, the angles marked as \(78^{\circ}\) and \(102^{\circ}\) in the intersections of the transversals with \(d\) and \(e\) follow the angle - relationships for parallel lines.

Step3: Analyze angles for problem 19

For lines \(a\), \(b\), \(c\), and \(d\) with transversal \(m\) in problem 19, lines \(a\), \(b\), and \(d\) have equal corresponding angles (e.g., the \(104^{\circ}\) and \(76^{\circ}\) angle - pairs). But line \(c\) has different angle measures (\(77^{\circ}\) and \(103^{\circ}\)) compared to the consistent angle pairs of \(a\), \(b\), and \(d\).

Step4: Analyze angles for problem 21

For lines \(S\), \(T\), \(D\), and \(E\) in problem 21, we can observe that the corresponding angles are equal. For instance, the \(43^{\circ}\) and \(137^{\circ}\) angle - pairs formed by the transversal show that \(S\parallel T\) and \(D\parallel E\).

Answer:

1. B. line \(d\parallel\) line \(e\)
2. C. line \(c\)
3. C. \(S\parallel T\&D\parallel E\)