parallel lines and planes dallas city hall i.m. pei parthenon athens havasu falls i.m. pei 3.1...
TRANSCRIPT
Parallel Lines and Planes
Dallas City HallI.M. Pei
ParthenonAthens
Havasu FallsI.M. Pei
3.1 Classroom Exercises
3.1 Classroom Exercises
8
5
7
62
4 3
1
1
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.
8 57 6
2
4
31
Name 2 pairs of Alternate interior angles.
1b
Note the Z points the way.Noted it is dyslexic.
8 57 6
2
4
31
Name 2 pairs of same-side interior angles.
1c
8 57 6
2
4
31
Name 2 pairs of same-side interior angles.
1c
Name 2 pairs of Alternate exterior angles.
1d
8 57 6
2
4
31
8 57 6
2
4
31
Name 2 pairs of same-side exterior angles.
1e
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
C’est fini.
Good day and good luck.