Question

Parallel Lines and Transversals

I. Refer to the figure at right.
1) Name two more pairs of parallel segments.
2) Name two more segments skew to NM
3) Name two transversals for parallel lines NO and PQ
4) Name a segment that is parallel to plane MRQ.
II. Identify the angles that go with the following types. (give all angles for each type)
5) Corresponding angles
6) Alternate exterior angles
8
7) Consecutive interior angles
8) Alternate interior angles
III. Using the figure below, state the transversal that forms each pair of angles. Then identify the

Answer 1

Parallel lines and Transversals

Correct responses:

1. $\overline{NP} \parallel \overline{OQ}$, $\overline{NO} \parallel \overline{PQ}$, $\overline{NR} \parallel \overline{OQ}$
2. $\overline{PQ}$ and $\overline{RQ}$
3. NP and OQ
4. MO
5. ∠4 and ∠5, ∠1, and ∠8; ∠3 and ∠6, ∠7 and ∠2
6. ∠4 and ∠7, ∠1 and ∠6
7. ∠3 and ∠5, ∠2 and ∠8
8. ∠3 and ∠8, ∠5 and ∠2
9. ∠1 and ∠12      transversal = r, special name = Alternate exterior angles
10. Transversal = r, special name = Corresponding angles
11. Transversal = r, special name = Alternate interior angles
12. Transversal = m, special name = Alternate exterior angles
13. Transversal = k, special name = Corresponding angles
14. Transversal = t, special name = Consecutive interior angles
15. JF, FG, GH, HI, and IJ
16. FA, EJ, DI, and CH
17. BC
18. Plane ABC
19. JF, FG, GH, and IJ
20. JF, GH, FG, and AB
21. 102°
22. 102°
23. 78°
24. 133°
25. 47°
26. 47°
27. 133°
28. 102°

What are the relationships between the segments,  angles, and the measure of the angles?

I. 1) Pairs of parallel (║) lines are;

• $\overline{NP} \parallel \overline{OQ}$

• $\overline{NO} \parallel \overline{PQ}$

• $\overline{NR} \parallel \overline{OQ}$

2) Lines that are skew to NM are;

• $\overline{PQ}$ and $\overline{RQ}$

3) Two transversals for parallel lines NO and PQ are;

• NP and OQ

4) A segment that is parallel to plane MRQ;

• MO

5) Corresponding angles are;

• ∠4 and ∠5, ∠1, and ∠8

• ∠3 and ∠6, ∠7 and ∠2

6) The alternate exterior angles are;

• ∠4 and ∠7, ∠1 and ∠6

7) Consecutive interior angles are;

• ∠3 and ∠5, ∠2 and ∠8

8) Alternate interior angles are;

• ∠3 and ∠8, ∠5 and ∠2

9) ∠1 and ∠12      transversal = r, special name = Alternate exterior angles

10) ∠2 and ∠10   transversal = r, special name = Corresponding angles

11) ∠4 and ∠9      transversal = r, special name = Alternate interior angles

12) ∠6 and ∠3    transversal = m, special name = Alternate exterior angles

13) ∠14 and ∠10   transversal = k, special name = Corresponding angles

14) ∠7 and ∠13  transversal = t, special name = Consecutive interior angles

15) The segments skew to EB are;

• JF, FG, GH, HI, and IJ

16) The segments that seem parallel to BG are;

• FA, EJ, DI, and CH

17) The segments that seem parallel to GH is; BC

18) The planes that appear parallel to plane FGH is; Plane ABC

19) Four segments skew to CD are; JF, FG, GH, and IJ

20) Four segments skew to DI are; JF, GH, FG, and AB

21) ∠3 = 180° - 78° = 102°

22) ∠4 = ∠3 = 102°

23) ∠5 = ∠1 = 78°

24) ∠6 = 180° - 47° = 133°

25) ∠7 = 47°

26) ∠8 = 47°

27) ∠9 = ∠6 = 133°

28) ∠10 = ∠3 = 102°

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