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
3 Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
2 & 3
8 7 6 5
4321
Same-side interior angles
C points the way.
4 Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
3 & 7
8 7 6 5
4321
Alternate interior angles
Z points the way.
8 7 6 5
43215 & 7
5 Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
Corresponding anglesSame position on ladder
8 7 6 5
43211 & 3
6 Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
Corresponding anglesSame position on ladder
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
Corresponding anglesSame position on ladder
13Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
L
CB
A D
E
J
F
H
G
K
&DCH CBJ
Corresponding anglesSame position on ladder
L
CB
A D
E
J
F
H
G
K
14Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
&FCB CBL
Alternate interior angles
Z points the way.
L
CB
A D
E
J
F
H
G
K
15Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
&FCL BLC
Same-side interior angles
C points the way.
16Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
L
CB
A D
E
J
F
H
G
K
&HCB CBJ
Same-side interior angles
C points the way.
17Classify each pair of angles as either alternate interior, same-side interior, or corresponding.
L
CB
A D
E
J
F
H
G
K
&GCH GLJ
Corresponding anglesSame position on ladder
Alternate interior angles
Z points the way.
Corresponding anglesSame 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
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
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
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
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
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
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
EFTheorem 3.1If 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
//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.
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.
H
GF
E
D
CB
A
Yes No
sometimes
32 Two lines that are not coplanar ________ intersect.
Complete each statement with always, sometimes, or never.
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
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 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 NoYes
36 Two planes parallel to the same line are __________ parallel to each other.
Complete each statement with always, sometimes, or never.
NoYes
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.