Parallel Lines and Planes Dallas City Hall I.M. Pei Parthenon Athens Havasu Falls I.M. Pei 3.1 Written Exercises

1 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Alternate exterior angles Z points the way.

2 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

3 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Same-side interior angles C points the way.

4 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Alternate interior angles Z points the way.

5 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

6 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

7 Name the two lines and transversal that form each pair of angles.

8

9 Not appropriate Because the lines Are not parallel.

10 Name the two lines and transversal that form each pair of angles.

11 Name the two lines and transversal that form each pair of angles.

12 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

13 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

14 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Alternate interior angles Z points the way.

15 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Same-side interior angles C points the way.

16 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Same-side interior angles C points the way.

17 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

Alternate interior angles Z points the way. Corresponding angles Same position on ladder Same-side interior angles C points the way. Same-side exterior angles Alternate exterior angles

23 Name 5 lines that appear to be // to

24 Name 3 lines that appear to be // to

25 Name 4 lines that appear to be skew to

26 Name 2 planes that appear to be // to

26 Name 2 planes that appear to be // to

27 Name 4 planes that appear to be // to

27 Name 4 planes that appear to be // to

27 Name 4 planes that appear to be // to

28 How many pairs of parallel planes are shown?

28 How many pairs of parallel planes are shown?

28 How many pairs of parallel planes are shown?

28 How many pairs of parallel planes are shown?

29 Suppose the top and bottom of the box lie in parallel planes. Explain how Theorem 3.1 can be used to prove

29 Suppose the top and bottom of the box lie in parallel planes. Explain how Theorem 3.1 can be used to prove Theorem 3.1 If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel.

29 Suppose the top and bottom of the box lie in parallel planes. Explain how Theorem 3.1 can be used to prove Theorem 3.1 If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel. Are the lines of intersection of the transversal plane CDJI.

30 When there is a transversal of two lines, the 3 lines are __________ coplanar. Complete each statement with always, sometimes, or never. Since two points of each line are in the same plane, all the lines are in the same plane. Remember, if 2 points of a line are in the plane, then the whole line is in the plane. always

31 Three lines intersecting in one point are ___________ coplanar. Complete each statement with always, sometimes, or never. Yes

31 Three lines intersecting in one point are ___________ coplanar. Complete each statement with always, sometimes, or never. Yes No sometimes

32 Two lines that are not coplanar ________ intersect. Complete each statement with always, sometimes, or never. never Intersecting lines are always coplanar And Non-intersecting are never coplanar.

33 Two lines parallel to a third line are ________ parallel to each other Complete each statement with always, sometimes, or never. always

34 Two lines skew to a third line are __________ skew to each other. Complete each statement with always, sometimes, or never. Yes No sometimes

35 Two lines perpendicular to a third line are __________ perpendicular to each other. Complete each statement with always, sometimes, or never. sometimes No Yes

36 Two planes parallel to the same line are __________ parallel to each other. Complete each statement with always, sometimes, or never. No Yes sometimes

37 Complete each statement with always, sometimes, or never. Two planes parallel to the same plane are __________ parallel to each other. always

38 Lines in two parallel planes are _________ parallel to each other. Complete each statement with always, sometimes, or never. Yes No sometimes

39 Two lines parallel to the same plane are _________ parallel to each other. Complete each statement with always, sometimes, or never. sometimes Yes No

C’est fini. Good day and good luck.