Question

3.1 & 3.2 quiz: parallel lines, transversals, and special angle pairs
use the figure below for questions 1 - 6.

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.

1. (angle1) and (angle14) ________________; transversal: __
2. (angle4) and (angle10) ________________; transversal: __
3. (angle6) and (angle16) ________________; transversal: __
4. (angle7) and (angle12) ________________; transversal: __
5. (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

1. (angle1) and (angle6)
2. (angle5) and (angle6)
3. (angle6) and (angle8)
4. (angle2) and (angle3)
5. (angle4) and (angle7)
6. (angle3) and (angle6)

Explanation:

Step1: Recall parallel - plane concept

In a 3 - D figure, planes that do not intersect are parallel. If we assume a standard rectangular - prism - like figure for the first part, a plane parallel to plane DEF could be plane ABC (assuming a typical naming convention for a rectangular prism).

Step2: Recall parallel - segment concept

Segments that do not intersect and are in the same or parallel planes are parallel. A segment parallel to FC could be AE. A segment parallel to AB could be DC.

Step3: Recall skew - segment concept

Skew segments are non - parallel and non - intersecting. A segment skew to DE could be BC.

Step4: Recall angle - pair relationships

For ∠1 and ∠14, they are corresponding angles. The transversal is the line that intersects the two lines containing the angles, say line l.
For ∠4 and ∠10, they are alternate interior angles. The transversal is the intersecting line.
For ∠6 and ∠16, they are alternate exterior angles. The transversal is the relevant intersecting line.
For ∠7 and ∠12, they are consecutive (same - side) interior angles. The transversal is the intersecting line.
For ∠13 and ∠15, they are consecutive (same - side) exterior angles. The transversal is the intersecting line.

Step5: Recall congruent and supplementary angle - pair rules

If l || m:
For ∠1 and ∠6, they are supplementary as they are consecutive (same - side) interior angles.
For ∠5 and ∠6, they are supplementary as they form a linear pair.
For ∠6 and ∠8, they are congruent as they are vertical angles.
For ∠2 and ∠3, they are supplementary as they form a linear pair.
For ∠4 and ∠7, they are congruent as they are alternate interior angles.
For ∠3 and ∠6, they are congruent as they are alternate interior angles.

Answer:

1. Plane ABC
2. AE
3. DC
4. BC
5. Corresponding angles; Transversal: relevant intersecting line
6. Alternate interior angles; Transversal: relevant intersecting line
7. Alternate exterior angles; Transversal: relevant intersecting line
8. Consecutive (same - side) interior angles; Transversal: relevant intersecting line
9. Consecutive (same - side) exterior angles; Transversal: relevant intersecting line
10. Supplementary; Consecutive (same - side) interior angles
11. Supplementary; Linear pair
12. Congruent; Vertical angles
13. Supplementary; Linear pair
14. Congruent; Alternate interior angles
15. Congruent; Alternate interior angles