Question

name: as mullins date: per: geometry unit 3: parallel & perpendicular lines 3.1 & 3.2 quiz: 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) (corresponding) transversal: 6. (angle4) and (angle10) (alternate interior) 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)

Explanation:

Step1: Recall parallel - line and angle - pair concepts

Parallel lines have specific angle - pair relationships when intersected by a transversal. Corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and consecutive interior angles are supplementary.

Step2: Analyze questions 1 - 4

For a 3 - D figure, parallel segments are those that do not intersect and are in the same or parallel planes. For example, if we consider a rectangular prism - like figure, segments parallel to a given segment can be found by looking at opposite or corresponding edges.

Step3: Analyze questions 5 - 9

For angle - pair relationships:

• Corresponding angles are in the same relative position with respect to the parallel lines and the transversal.
• Alternate interior angles are between the parallel lines and on opposite sides of the transversal.
• For questions 10 - 15, we use the properties of parallel lines \(l\parallel m\). If two parallel lines are cut by a transversal:
• Alternate interior angles, alternate exterior angles, and corresponding angles are congruent.
• Consecutive interior angles are supplementary.

Question 1 - 4 (assuming a rectangular - prism like figure):

1. A plane parallel to plane \(DEF\) could be plane \(ABC\) (assuming a standard 3 - D rectangular - prism naming convention).
2. A segment parallel to \(FC\) could be \(AE\).
3. A segment parallel to \(AB\) could be \(DE\).
4. A segment skew to \(DB\) could be \(CE\) (skew lines are non - parallel and non - intersecting in 3 - D space).

Question 5 - 9:

1. \(\angle1\) and \(\angle14\) are corresponding angles. The transversal is the line that intersects the two lines containing \(\angle1\) and \(\angle14\).
2. \(\angle4\) and \(\angle10\) are alternate interior angles. The transversal is the line that intersects the two lines containing \(\angle4\) and \(\angle10\).
3. If \(\angle6\) and \(\angle16\) are in a parallel - line and transversal setup, if they are in the same relative position with respect to the parallel lines and the transversal, they are corresponding angles. The transversal is the intersecting line.
4. If \(\angle7\) and \(\angle12\) are between the parallel lines and on opposite sides of the transversal, they are alternate interior angles. The transversal is the intersecting line.
5. If \(\angle13\) and \(\angle15\) are between the parallel lines and on the same side of the transversal, they are consecutive (same - side) interior angles. The transversal is the intersecting line.

Question 10 - 15:

1. If \(l\parallel m\), and \(\angle1\) and \(\angle8\) are alternate exterior angles, they are congruent.
2. If \(\angle5\) and \(\angle6\) are consecutive (same - side) interior angles, they are supplementary.
3. If \(\angle6\) and \(\angle8\) are vertical angles (assuming they are formed by the intersection of two lines), they are congruent.
4. If \(\angle2\) and \(\angle3\) are vertical angles, they are congruent.
5. If \(\angle4\) and \(\angle7\) are alternate interior angles, they are congruent.
6. If \(\angle3\) and \(\angle6\) are consecutive (same - side) interior angles, they are supplementary.

Answer:

1. Plane \(ABC\)
2. Segment \(AE\)
3. Segment \(DE\)
4. Segment \(CE\)
5. Corresponding angles; Transversal: [the intersecting line]
6. Alternate interior angles; Transversal: [the intersecting line]
7. Corresponding angles; Transversal: [the intersecting line] (assuming appropriate parallel - line and transversal setup)
8. Alternate interior angles; Transversal: [the intersecting line]
9. Consecutive (same - side) interior angles; Transversal: [the intersecting line]
10. Congruent; Alternate exterior angles
11. Supplementary; Consecutive (same - side) interior angles
12. Congruent; Vertical angles
13. Congruent; Vertical angles
14. Congruent; Alternate interior angles
15. Supplementary; Consecutive (same - side) interior angles