Parallel Lines and Planes
Dallas City HallI.M. Pei
ParthenonAthens
Havasu FallsI.M. Pei
3.1 Classroom Exercises
ExteriorExterior
interior
1
34
2 6
7
5
8
This is a bad diagram because corresponding angles are only important when you have parallel lines.
Let’s adjust the picture.
1
Name 4 pairs of corresponding angles.
8 57 6
2
4
31
Upper left hand corners.
Upper right hand corners.
Lower left hand corners.
Lower right hand corners.
1a
Think of same step on a ladder.
8 57 6
2
4
31
Name 2 pairs of Alternate interior angles.
1b
Note the Z points the way.Noted it is dyslexic.
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
16151413
1211109
875 6
4321
7 11and Same-side interior angles
C points the way.
2
16151413
1211109
875 6
4321
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
14 16and corresponding anglesSame Ladder Position
3
16151413
1211109
875 6
4321
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
4 10and None.
Note 4 lines not 3 lines are involved.
4
Alternate Interior anglesAIA
16151413
1211109
875 6
4321
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
3 6and
5
Note the Z points the way.
16151413
1211109
875 6
4321
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
6 11and None.
Note 4 lines not 3 lines are involved.
6
16151413
1211109
875 6
4321
Corresponding anglesSame Ladder Position
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
2 10and
7
16151413
1211109
875 6
4321
Same-side interior angles
C points the way.
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
2 3and
8
16151413
1211109
875 6
4321
Alternate interior anglesAIA
Classify each pair of angles as either corresponding anglesalternate interior angles, alternate exterior angles,Same-side interior angles,Same-side exterior angles,None of these.
7 12and
9
Note the Z points the way.
Classify each pair of lines as intersecting, parallel, or skew.
AB and EJ�������������������������� ��
G
FH
IE
A D
CB
J N
MK
L
Parallel
10a
Classify each pair of lines as intersecting, parallel, or skew.
AB and FK�������������������������� ��
G
FH
IE
A D
CB
J N
MK
L
Parallel
10b
Classify each pair of lines as intersecting, parallel, or skew.
AB and ID�������������������������� ��
G
FH
IE
A D
CB
J N
MK
L
Skew
10c
Classify each pair of lines as intersecting, parallel, or skew.
EF and IH�������������������������� ��
G
FH
IE
A D
CB
J N
MK
L
IntersectingNote that they are in the same plane.
10d
Classify each pair of lines as intersecting, parallel, or skew.
EF and NM�������������������������� ��
G
FH
IE
A D
CB
J N
MK
L
Skew
10e
Classify each pair of lines as intersecting, parallel, or skew.
CN and FG�������������������������� ��
G
FH
IE
A D
CB
J N
MK
L
Skew
10f
Name 6 lines // to
G
FH
IE
A D
CB
J N
MK
LGL������������� �
FK������������� �
EJ������������� �AB������������� �DC������������� �IN������������� �HM������������� � 11
Name several lines skew to
G
FH
IE
A D
CB
J N
MK
LGL������������� �
NC������������� �
BC������������� �
AD������������� �
AE������������� �
JB������������� �
EF������������� �
HI������������� �
ID������������� �
12
Name 5 lines // to ABCD
G
FH
IE
A D
CB
J N
MK
L
FK������������� �EJ������������� �IN������������� �HM������������� �
13
GL������������� �
Name coplanar segmentsthat do not intersect andyet are not parallel. G
FH
IE
A D
CB
J N
MK
L
EF and������������� �
HI������������� �
JB and������������� �
LM������������� �
14
Complete each statement with the word…
always, sometimes or never
Two skew lines are _________ parallel.neverSkew lines are non-coplanar while parallel lines are coplanar.
Two parallel lines are _________ coplanar.always
It is a requirement of definitions.
15
16
Complete each statement with the word…
always, sometimes or never
A line in the plane of the ceiling and a line in the floor are ____________ parallel.sometimes
H
GF
E
D
CB
A
Parallel
Skew
17
H
GF
E
D
CB
A
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ parallel.
Yes
18
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ parallel.
H
GF
E
D
CB
A
Yes again
18
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ parallel.Sometimes
H
GF
E
D
CB
A
No.
18
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ intersecting.
H
GF
E
D
CB
A
Yes
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ intersecting.Sometimes
H
GF
E
D
CB
A
No
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ skew.
H
GF
E
D
CB
A
No
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ skew.
H
GF
E
D
CB
A
Yes
Sometimes
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ skew.Sometimes
H
GF
E
D
CB
A
No again
Complete each statement with the word…
always, sometimes or never
A line in the plane of the wall and the plane of the floor are __________ skew.Sometimes
H
GF
E
D
CB
A
Yes again