Parallel Lines and Planes

Parallel Lines and Planes

Dallas City HallI.M. Pei

ParthenonAthens

Havasu FallsI.M. Pei

3.1 Written Exercises

3.1 Written Exercises1 Classify each pair of angles as either alternate interior,

same-side interior, or corresponding.

2 & 6

8 7 6 5

4321

Alternate exterior angles

Z points the way.

2 Classify each pair of angles as either alternate interior, same-side interior, or corresponding.

8 & 6

8 7 6 5

4321

Corresponding anglesSame position on ladder


2 & 3

8 7 6 5

4321

Same-side interior angles

C points the way.


3 & 7

8 7 6 5

4321

Alternate interior angles

Z points the way.

8 7 6 5

43215 & 7



8 7 6 5

43211 & 3



2 & 3

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

5

43

21

P Q

S R

,

,

PQ

SR

SQ

��

��

��

1 & 4 8 Name the two lines and transversal that form each pair of

angles.

5

43

21

P Q

S R

,

,

PS

QR

SQ

��

��

��

&P PSR

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

5

43

21

P Q

S R

Not appropriateBecause the linesAre not parallel.

5 & PSR 10 Name the two lines and transversal that form each pair of

angles.

5

43

21

P Q

S R

,

,

PS

QR

SR

��

��

��

5 & PQR 11 Name the two lines and transversal that form each pair of

angles.

5

43

21

P Q

S R

,

,

PQ

SR

QR

��

��

��

L

CB

A D

E

J

F

H

G

K

12Classify each pair of angles as either alternate interior, same-side interior, or corresponding.

&EBA FCB



L

CB

A D

E

J

F

H

G

K

&DCH CBJ


L

CB

A D

E

J

F

H

G

K


&FCB CBL


Z points the way.

L

CB

A D

E

J

F

H

G

K


&FCL BLC


C points the way.


L

CB

A D

E

J

F

H

G

K

&HCB CBJ


C points the way.


L

CB

A D

E

J

F

H

G

K

&GCH GLJ



Z points the way.



C points the way.

Same-side exterior angles

Alternate exterior angles

23 Name 5 lines that appear to be // to

L K

H I

GJ

DA

CB

EF

AG

24 Name 3 lines that appear to be // to

L K

H I

GJ

DA

CB

EF

AB

25 Name 4 lines that appear to be skew to

L K

H I

GJ

DA

CB

EF

AB

26 Name 2 planes that appear to be // to

L K

H I

GJ

DA

CB

EF

AF

26 Name 2 planes that appear to be // to AF

L K

H I

GJ

DA

CB

EF

27 Name 4 planes that appear to be // to

L K

H I

GJ

DA

CB

EF

FL

27 Name 4 planes that appear to be // to FL

L K

H I

GJ

DA

CB

EF

27 Name 4 planes that appear to be // to FL

L K

H I

GJ

DA

CB

EF

28 How many pairs of parallel planes are shown?

L K

H I

GJ

DA

CB

EF


L K

H I

GJ

DA

CB

EF

L K

H I

GJ

DA

CB

EF


L K

H I

GJ

DA

CB

EF

L K

H I

GJ

DA

CB

EF

L K

H I

GJ

DA

CB

EF


L K

H I

GJ

DA

CB

EF

L K

H I

GJ

DA

CB

EF

L K

H I

GJ

DA

CB

EF

L K

H I

GJ

DA

CB

EF

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

L K

H I

GJ

DA

CB

EF


L K

H I

GJ

DA

CB

EFTheorem 3.1If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel.


//CD IJL K

H I

GJ

DA

CB

EFTheorem 3.1If 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.


Yes

31 Three lines intersecting in one point are___________ coplanar.


H

GF

E

D

CB

A

Yes No

sometimes

32 Two lines that are not coplanar ________ intersect.


never

Intersecting lines are always coplanarAnd

Non-intersecting are never coplanar.

L K

H I

GJ

DA

CB

EF

33 Two lines parallel to a third line are ________ parallel to each other


always

34 Two lines skew to a third line are __________ skew to each other.


Yes No No

sometimes

35 Two lines perpendicular to a third line are __________ perpendicular to each other.


sometimes

No NoYes

36 Two planes parallel to the same line are __________ parallel to each other.


NoYes

sometimes

37


Two planes parallel to the same plane are __________ parallel to each other.always

38 Lines in two parallel planes are _________ parallel to each other.


Yes No

sometimes

39 Two lines parallel to the same plane are _________ parallel to each other.


sometimes

Yes No

C’est fini.

Good day and good luck.

Parallel Lines and Planes

Documents

pair of angles

interior angles c points

parallel lines

pairs of parallel planes

alternate exterior anglesz

lines of intersection

written exercises3

written exercises1classify