24
Millau Bridge Sir Norman Foster Point, Lines, Planes, Angles Fallingwaters Frank Lloyd Wright Millenium Park Frank Lloyd Wright 1.2 CE Points, Lines, and Planes
Millau BridgeSir Norman Foster
Point, Lines, Planes, Angles
FallingwatersFrank Lloyd Wright
Millenium ParkFrank Lloyd Wright
1.2 CE Points, Lines, and Planes
1.2 CE Points, Lines, and PlanesClassify each statement as true or false.
1 int sec . .XY er ts planeM at pt O�������������� �
2 int sec
.
PlaneM er ts XY
inmorethanone pt
�������������� �
3 T, O, and R are collinear.
4
5
6
X, O, and Y are collinear.
R, O, S, and W are coplanar.
R, S, T, and X are coplanar.
7 R, X, O, and Y are coplanar.
M
OR
ST
W
X
Y
True
False, only O
1.2 CE Points, Lines, and PlanesClassify each statement as true or false.
2 int sec
.
PlaneM er ts XY
inmorethanone pt
�������������� �
3 T, O, and R are collinear.
4
5
6
X, O, and Y are collinear.
R, O, S, and W are coplanar.
R, S, T, and X are coplanar.
7 R, X, O, and Y are coplanar.
M
OR
ST
W
X
Y
False, only O
1.2 CE Points, Lines, and PlanesClassify each statement as true or false.
2 int sec
.
PlaneM er ts XY
inmorethanone pt
�������������� �
3 T, O, and R are collinear.
4
5
6
X, O, and Y are collinear.
R, O, S, and W are coplanar.
R, S, T, and X are coplanar.
7 R, X, O, and Y are coplanar.
M
OR
ST
W
X
Y
False, only O
False, curved line
1.2 CE Points, Lines, and PlanesClassify each statement as true or false.
2 int sec
.
PlaneM er ts XY
inmorethanone pt
�������������� �
3 T, O, and R are collinear.
4
5
6
X, O, and Y are collinear.
R, O, S, and W are coplanar.
R, S, T, and X are coplanar.
7 R, X, O, and Y are coplanar.
M
OR
ST
W
X
Y
False, only O
False, curved line
True
1.2 CE Points, Lines, and PlanesClassify each statement as true or false.
2 int sec
.
PlaneM er ts XY
inmorethanone pt
�������������� �
3 T, O, and R are collinear.
4
5
6
X, O, and Y are collinear.
R, O, S, and W are coplanar.
R, S, T, and X are coplanar.
M
OR
ST
W
X
Y
False, only O
False, curved line
True
True. They are all in the yellow plane.
1.2 CE Points, Lines, and PlanesClassify each statement as true or false.
2 int sec
.
PlaneM er ts XY
inmorethanone pt
�������������� �
3 T, O, and R are collinear.
4
5
6
X, O, and Y are collinear.
R, O, S, and W are coplanar.
R, S, T, and X are coplanar.
M
OR
ST
W
X
Y
False, only O
False, curved line
True
True. They are all in the yellow plane.
False, R, S, and T are in the yellow plane but X is not.
1.2 CE Points, Lines, and PlanesClassify each statement as true or false.
5
6
R, O, S, and W are coplanar.
R, S, T, and X are coplanar.
7 R, X, O, and Y are coplanar.
M
OR
ST
W
X
Y
True. They are all in the yellow plane.
False, R, S, and T are in the yellow plane but X is not.
True. They are all in the vertical green plane.
1.2 CE Points, Lines, and Planes
8
M
OR
ST
W
X
Y
Does a plane have edges?
No. What we draw is only a model.The real plane extends outward forever.
1.2 CE Points, Lines, and Planes9
Can a given point be in two lines?
Ten lines?
M
OR
ST
W
X
Y
Yes. On the right O is on three lines.
Yes
H
RL
B
AA
B
A
A
F
ED
CB
A
1.2 CE Points, Lines, and Planes
10
Can a given line be in two planes?
Ten planes?
Yes AD�������������� �
Yes. Think of pages in a book.
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
11. A, B, C
16. B, G, C
12. E, F, H
13. D, C, H
14. A, D, E
15. B, E, F
D
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
11. A, B, C
16. B, G, C
12. E, F, H
13. D, C, H
14. A, D, E
15. B, E, F
D
G
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
11. A, B, C
16. B, G, C
12. E, F, H
13. D, C, H
14. A, D, E
15. B, E, F
D
G
G
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
11. A, B, C
16. B, G, C
12. E, F, H
13. D, C, H
14. A, D, E
15. B, E, F
D
G
G
H
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
11. A, B, C
16. B, G, C
12. E, F, H
13. D, C, H
14. A, D, E
15. B, E, F
D
G
G
H
A
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
11. A, B, C
16. B, G, C
12. E, F, H
13. D, C, H
14. A, D, E
15. B, E, F
D
G
G
H
A
F
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
A, D, G
E, H, C
D, F, H
F
Unusual examples.
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
A, D, G
E, H, C
D, F, H
F
Unusual examples.
B
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Name the fourth point that is in the same plane as the given points.
A, D, G
E, H, C
D, F, H
F
Unusual examples.
B
B
F
GH
E
B
CD
A
Q17. Are there any points on
besides C and G?
Q18. Are there more than 4 points in plane ABCD?
Yes. There are an infinite number of pts. They are just not labeled.
Yes. There are an infinite number of pts. They are just not labeled.
F
GH
E
B
CD
A
Q19. Name the intersection of
planes ABFE and BCGF.
F
GH
E
B
CD
A
FB�������������� �
F
GH
E
B
CD
A
F
GH
E
B
CD
A
F
GH
E
B
CD
A
Q20. Name 2 planes that
do not intersect.
ABCD & EFGH
ADHE & BCGF
ADFE & DCGH
C’est fini.
Good day and good luck.
