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.
 2 & 6
1
8 7
2
3 4
6 5
Alternate exterior angles
Z points the way.
2
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
8 &  6
1
8 7
2
3 4
6 5
Corresponding angles
Same position on ladder
3
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
 2 & 3
1
8 7
2
3 4
6 5
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
1
8 7
2
3 4
6 5
Alternate interior angles
Z points the way.
5
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
5 & 7
1
8 7
2
3 4
6 5
Corresponding angles
Same position on ladder
6
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
1 &  3
1
8 7
2
3 4
6 5
Corresponding angles
Same position on ladder
7
Name the two lines and transversal that form each pair of
angles.
 2 & 3
P
Q
PQ ,
3
1
SR ,
S
SQ
4
5
2
R
8
Name the two lines and transversal that form each pair of
angles.
1 &  4
P
Q
PS ,
3
1
QR ,
S
SQ
4
5
2
R
9
Name the two lines and transversal that form each pair of
angles.
 P &  PSR
P
Q
3
Not appropriate
Because the lines
Are not parallel.
1
S
4
5
2
R
10
Name the two lines and transversal that form each pair of
angles.
 5 &  PSR
P
Q
PS ,
3
1
QR ,
S
SR
4
5
2
R
11
Name the two lines and transversal that form each pair of
angles.
 5 &  PQR
P
PQ ,
3
SR ,
QR
Q
1
S
4
5
2
R
12
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
E
F
A
G
C
D
B
 EBA &  FCB
Corresponding angles
Same position on ladder
L
H
K
J
13
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
E
F
A
G
C
D
B
 DCH &  CBJ
Corresponding angles
Same position on ladder
L
H
K
J
14
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
E
F
A
G
C
D
B
 FCB &  CBL
Alternate interior angles
Z points the way.
L
H
K
J
15
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
E
F
A
G
C
D
B
 FCL &  BLC
Same-side interior angles
C points the way.
L
H
K
J
16
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
E
F
A
G
C
D
B
 HCB &  CBJ
Same-side interior angles
L
C points the way.
H
K
J
17
Classify each pair of angles as either alternate interior,
same-side interior, or corresponding.
E
F
A
G
C
D
B
 GCH &  GLJ
Corresponding angles
Same position on ladder
L
H
K
J
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
AG
F
E
A
D
B
C
L
K
G
J
H
I
24
Name 3 lines that appear to be // to
AB
F
E
A
D
B
C
L
K
G
J
H
I
25
Name 4 lines that appear to be skew to
F
AB
E
A
D
B
C
L
K
G
J
H
I
26
Name 2 planes that appear to be // to
F
AF
E
A
D
B
C
L
K
G
J
H
I
26
Name 2 planes that appear to be // to
F
AF
E
A
D
B
C
L
K
G
J
H
I
27
Name 4 planes that appear to be // to
F
FL
E
A
D
B
C
L
K
G
J
H
I
27
Name 4 planes that appear to be // to
FL
F
E
A
D
B
C
L
K
G
J
H
I
27
Name 4 planes that appear to be // to
FL
F
E
A
D
B
C
L
K
G
J
H
I
28
How many pairs of parallel planes are shown?
F
E
A
D
B
C
L
K
G
J
H
I
28
How many pairs of parallel planes are shown?
F
E
F
A
D
B
D
B
K
C
L
G
J
H
A
C
L
E
I
K
G
J
H
I
28
How many pairs of parallel planes are shown?
F
F
E
E
A
A
D
B
D
B
C
L
C
L
K
K
G
G
J
J
H
F
I
E
H
A
D
B
C
L
K
G
J
H
I
I
28
How many pairs of parallel planes are shown?
F
F
E
E
A
A
D
D
B
B
C
C
L
L
K
K
G
G
J
J
H
I
H
I
F
E
A
D
B
F
E
A
C
D
B
L
C
K
L
G
J
H
K
G
J
I
H
I
29
Suppose the top and bottom of the box lie in
parallel planes. Explain how Theorem 3.1 can
be used to prove
F
E
A
D
B
C
L
K
G
J
H
I
29
Suppose the top and bottom of the box lie in
parallel planes. Explain how Theorem 3.1 can
be used to prove
F
Theorem 3.1
If 2 parallel planes are cut by
a third plane, then the lines
of intersection are parallel.
E
A
D
B
C
L
K
G
J
H
I
29
Suppose the top and bottom of the box lie in
parallel planes. Explain how Theorem 3.1 can
be used to prove
F
Theorem 3.1
If 2 parallel planes are cut by
a third plane, then the lines
of intersection are parallel.
E
A
D
B
C
CD // IJ
Are the lines of
intersection of the
transversal plane CDJI.
L
K
G
J
H
I
Complete each statement with
always, sometimes, or never.
30
When there is a transversal of two lines, the 3
always coplanar.
lines are __________
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.
31
Three lines intersecting in one point are
___________ coplanar.
Yes
Complete each statement with
always, sometimes, or never.
31
Three lines intersecting in one point are
___________
sometimes coplanar.
C
B
A
F
E
Yes
D
G
H
No
Complete each statement with
always, sometimes, or never.
32
never
Two lines that are not coplanar ________
intersect.
Intersecting lines are always coplanar
And
Non-intersecting 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
F
E
A
D
B
C
L
K
G
J
H
I
Complete each statement with
always, sometimes, or never.
34
sometimes
Two lines skew to a third line are __________
skew to each other.
Yes
No
No
Complete each statement with
always, sometimes, or never.
35
Two lines perpendicular to a third line are
sometimes perpendicular to each other.
__________
No
Yes
No
Complete each statement with
always, sometimes, or never.
36
Two planes parallel to the same line are
sometimes parallel to each other.
__________
Yes
No
Complete each statement with
always, sometimes, or never.
37
Two planes parallel to the same plane are
always parallel to each other.
__________
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
sometimes
_________ parallel to each other.
Yes
No
C’est fini.
Good day and good luck.