Question

consider the lines that contain segments in the figure. all angles are right angles.

1. line(s) parallel to cd.
2. line(s) perpendicular to cd.

use the diagram to answer the following.

1. name a pair of parallel lines.
2. name a pair of perpendicular lines.
3. is pn || km? explain.
4. is pr ⊥ np? explain.

identify all pairs of angles of the given type.

1. corresponding.
2. alternate interior.
3. alternate exterior.
4. consecutive interior.

classify the angle pair.

1. ∠5 and ∠1
2. ∠11 and ∠13
3. ∠6 and ∠13
4. ∠2 and ∠11

Explanation:

Step1: Recall parallel - line definition

Parallel lines are lines that never intersect in a plane. In a rectangular - prism (for the first figure), lines parallel to CD are those with the same direction. In the second set of lines, parallel lines have the same slope.

Step2: Recall perpendicular - line definition

Perpendicular lines intersect at a right angle (90 degrees).

Step3: Recall angle - pair definitions

Corresponding angles are in the same relative position at each intersection where a transversal crosses two lines. Alternate interior angles are between the two lines and on opposite sides of the transversal. Alternate exterior angles are outside the two lines and on opposite sides of the transversal. Consecutive interior angles are between the two lines and on the same side of the transversal.

For the rectangular - prism:

1. Lines parallel to CD are AB, EF, and GH.
2. Lines perpendicular to CD are AD, BC, FG, and EH.

For the set of lines with transversals:

1. A pair of parallel lines could be LM and KN.
2. A pair of perpendicular lines could be PN and PR.
3. PN is not parallel to KM because they intersect at a non - zero angle (not 0 or 180 degrees).
4. PR is perpendicular to NP as they intersect at a right angle.
5. Corresponding angles: ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8.
6. Alternate interior angles: ∠3 and ∠6, ∠4 and ∠5.
7. Alternate exterior angles: ∠1 and ∠8, ∠2 and ∠7.
8. Consecutive interior angles: ∠3 and ∠5, ∠4 and ∠6.

For the last set of angle pairs:

1. ∠5 and ∠1 are corresponding angles.
2. ∠11 and ∠13 are vertical angles.
3. ∠6 and ∠13 are alternate interior angles.
4. ∠2 and ∠11 are alternate exterior angles.

Answer:

1. AB, EF, GH
2. AD, BC, FG, EH
3. LM and KN
4. PN and PR
5. No, they intersect at a non - zero angle.
6. Yes, they intersect at a right angle.
7. ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8
8. ∠3 and ∠6, ∠4 and ∠5
9. ∠1 and ∠8, ∠2 and ∠7
10. ∠3 and ∠5, ∠4 and ∠6
11. Corresponding angles
12. Vertical angles
13. Alternate interior angles
14. Alternate exterior angles