Question

per: __ unit 3: parallel & perpendicular lines homework: parallel lines, transversals, and special angle pairs use the figure below for questions 1 - 4. 1. name a plane parallel to plane def. 2. name a segment parallel to (overline{fc}). 3. name a segment parallel to (overline{ab}). 4. name a segment skew to (overline{de}). using the diagram to the right for questions 5 - 9, classify the angle - pair relationship as corresponding, alternate interior, alternate exterior, consecutive (same - side) interior angles, or consecutive (same - side) exterior angles. then, name the transversal that connects them. 5. (angle1) and (angle14) __________; transversal: 6. (angle4) and (angle10) __________; transversal: 7. (angle6) and (angle16) __________; transversal: 8. (angle7) and (angle12) __________; transversal: 9. (angle13) and (angle15) __________; transversal: __ if (lparallel m), identify the angle pair as congruent or supplementary. justify your reasoning by classifying the angle pair. angle pair congruent or supplementary? classify 10. (angle1) and (angle8) 11. (angle5) and (angle6) 12. (angle6) and (angle8) 13. (angle2) and (angle3) 14. (angle4) and (angle7) 15. (angle3) and (angle6) © gina wilson (all things algebra®, llc), 2014 - 2019

Explanation:

Step1: Recall parallel - plane concept

In a three - dimensional figure, planes that do not intersect are parallel. For the first question, plane $ABC$ is parallel to plane $DEF$.

Step2: Recall parallel - segment concept

Segments that lie in parallel planes or are part of parallel lines are parallel. For the second question, $\overline{AD}$ is parallel to $\overline{FC}$ as they are part of parallel lines in the 3 - D figure. For the third question, $\overline{DE}$ is parallel to $\overline{AB}$.

Step3: Recall skew - segment concept

Skew segments are non - parallel and non - intersecting. For the fourth question, $\overline{AC}$ is skew to $\overline{DE}$ as they are in different non - parallel planes and do not intersect.

Step4: Recall angle - pair relationships

For question 5: $\angle1$ and $\angle14$ are alternate exterior angles. The transversal is $r$.
For question 6: $\angle4$ and $\angle10$ are alternate interior angles. The transversal is $r$.
For question 7: $\angle6$ and $\angle16$ are corresponding angles. The transversal is $s$.
For question 8: $\angle7$ and $\angle12$ are consecutive (same - side) interior angles. The transversal is $r$.
For question 9: $\angle13$ and $\angle15$ are consecutive (same - side) exterior angles. The transversal is $s$.

Step5: Recall congruent and supplementary angle pairs

For question 10: $\angle1$ and $\angle8$ are alternate exterior angles. When $l\parallel m$, alternate exterior angles are congruent.
For question 11: $\angle5$ and $\angle6$ are consecutive (same - side) interior angles. When $l\parallel m$, consecutive (same - side) interior angles are supplementary.
For question 12: $\angle6$ and $\angle8$ are vertical angles. Vertical angles are congruent.
For question 13: $\angle2$ and $\angle3$ are consecutive (same - side) interior angles. When $l\parallel m$, consecutive (same - side) interior angles are supplementary.
For question 14: $\angle4$ and $\angle7$ are alternate interior angles. When $l\parallel m$, alternate interior angles are congruent.
For question 15: $\angle3$ and $\angle6$ are alternate interior angles. When $l\parallel m$, alternate interior angles are congruent.

Answer:

1. Plane $ABC$
2. $\overline{AD}$
3. $\overline{DE}$
4. $\overline{AC}$
5. Alternate exterior angles; $r$
6. Alternate interior angles; $r$
7. Corresponding angles; $s$
8. Consecutive (same - side) interior angles; $r$
9. Consecutive (same - side) exterior angles; $s$
10. Congruent; Alternate exterior angles
11. Supplementary; Consecutive (same - side) interior angles
12. Congruent; Vertical angles
13. Supplementary; Consecutive (same - side) interior angles
14. Congruent; Alternate interior angles
15. Congruent; Alternate interior angles