Parthenon Athens

Dallas City Hall I.M. Pei

Havasu Falls I.M. Pei

Parallel Lines and Planes

3.1 Written Exercises

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

Name the two lines and transversal that form each

pair of angles.

9

Name the two lines and transversal that form each

pair of angles.

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.

Classify each pair of angles as either alternate

interior, same-side interior, or corresponding.

12

Corresponding angles Same position on ladder

Classify each pair of angles as either alternate

interior, same-side interior, or corresponding.

13

Corresponding angles Same position on ladder

Classify each pair of angles as either alternate

interior, same-side interior, or corresponding.

14

Alternate interior angles Z points the way.

Classify each pair of angles as either alternate

interior, same-side interior, or corresponding.

15

Same-side interior angles C points the way.

Classify each pair of angles as either alternate

interior, same-side interior, or corresponding.

16

Same-side interior angles C points the way.

Classify each pair of angles as either alternate

interior, same-side interior, or corresponding.

17

Corresponding angles Same position on ladder

Alternate exterior angles

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

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.

Complete each statement with always, sometimes,

or never.

30

When there is a transversal of two lines, the 3

lines are __________ coplanar.

always

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.

Complete each statement with always, sometimes,

or never.

Three lines intersecting in one point

are ___________ coplanar.

31

Yes

Complete each statement with always, sometimes,

or never.

Three lines intersecting in one point

are ___________ coplanar.

31

sometimes

No

Yes

Complete each statement with always, sometimes,

or never.

32

never

Two lines that are not coplanar ________

intersect.

Intersecting lines are always coplanar And Non-int

ersecting are never coplanar.

Complete each statement with always, sometimes,

or never.

33

always

Two lines parallel to a third line are ________

parallel to each other

Complete each statement with always, sometimes,

or never.

sometimes

34

Two lines skew to a third line are __________

skew to each other.

No

No

Yes

Complete each statement with always, sometimes,

or never.

35

Two lines perpendicular to a third line are

__________ perpendicular to each other.

sometimes

No

Yes

No

Complete each statement with always, sometimes,

or never.

36

Two planes parallel to the same line are

__________ parallel to each other.

sometimes

Yes

No

Complete each statement with always, sometimes,

or never.

37

Two planes parallel to the same plane are

__________ parallel to each other.

always

Complete each statement with always, sometimes,

or never.

38

sometimes

Lines in two parallel planes are _________

parallel to each other.

Yes

No

Complete each statement with always, sometimes,

or never.

39

Two lines parallel to the same plane are

_________ parallel to each other.

sometimes

Yes

No

Cest fini.

Good day and good luck.