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Millau Bridge Sir Norman Foster Point, Lines, Planes, Angles Fallingwaters Frank Lloyd Wright Millenium Park Frank Lloyd Wright 1.2 WE Points, Lines and Planes
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Millau BridgeSir Norman Foster
Point, Lines, Planes, Angles
FallingwatersFrank Lloyd Wright
Millenium ParkFrank Lloyd Wright
1.2 WE Points, Lines and Planes
1.2 WE Points, Lines and PlanesTrue or False
h
S
RD
A
B
C1 .ABis in plane R�������������� �
2 .S contains AB�������������� �
3 .Rand S containD
4 .Dis onlineh 5 .his in S
Yes.
Yes, the planes extend to include the whole line.
Yes, the planes extend to include the whole line.
Yes. Yes.
True or False
h
S
RD
A
B
C
7 int secPlane R er ts
plane S in AB�������������� �
8 . .Pt C is in R and S
9 , , .A B and C arecollinear10 , , ,
.
A B C and D
arecoplanar
6 .his in R No. It only passes thru plane R.
Yes.
No. it is only in Plane S.
No. No straight line will contain all 3 pts.
Yes. They are all in plane S.
P
P11. Make a sketch showing 4 coplanar points such that 3, but not 4 are collinear.
12. Make a sketch showing 4 points that are not coplanar.
R S
WT
V13. Name 5 planes that contain sides of the pyramid shown.
14. Of the 5 planes, are there any that do not intersect?
15. Name 3 lines that intersect with R.
VRS, VST, VWT, VWR, RSTW
Sides
Bottom
No. 4 intersect at point V and the bottom intersects all the sides.
RW, RS, RV
R S
WT
V16. Name 2 planes that intersect in .
17. Name 3 planes that intersect at point S.
18. Name a line and a plane that intersect in a point.
ST�������������� �
STV, STWVNote all planes contain S and T.
STV, SRV, STWR
,VS RSTW�������������� �
or ,RS VST�������������� �
And many Others.
Follow the steps shown to draw the figure named.
Rectangular solid or box.19
20Follow the steps shown to draw the figure named.
A barn.
B
F
A
E
R
S
H
D
G
C
21. Name 2 planes that intersect in FG�������������� �
22. Name 3 lines that intersect at pt. E.
23. Name 3 plane that intersect at pt. B.
24a. Are points A, D, and C collinear?
24b. Are points A, D, and C coplanar?
FGSR and FGCB the roof and right side.
, ,ER ES EA������������������������������������������������������������������ �����
ABCE, ABFRE, BCGF
Front,Right Side,Floor
No.
Yes. The floor.
B
F
A
E
R
S
H
D
G
C
25a. Are points R, S, G, and F coplanar?
25b. Are points R, S, G, and C coplanar?
26a. Name 2 planes that do not intersect.
26a. Name 2 other planes that do not intersect.
Yes – the yellow plane.
No – C is not on the yellow plane.
ABFRE and DCGSEThe front and back
BCGF and ADHEThe right and left sides.
28a. Can 2 vertical planes intersect?
28b. Suppose a line is known to be in a vertical plane. Does the line have to be a vertical line?
27. Can 2 horizontal planes intersect?
Yes. Look at the two walls in the corner of the room.
No. Two floors of a building do not intersect.
NO. Look at cinderblock wall or a brick wall. They are vertical but they contain horizontal joint lines.
Sketch and label the figures described. Use dashes for hidden lines.29. Vertical line l intersects a horizontal plane M at point A.
M
l
A
Sketch and label the figures described. Use dashes for hidden lines.29. Vertical line l intersects a horizontal plane M at point A.
Sketch and label the figures described. Use dashes for hidden lines.
30. Horizontal plane P contains two lines k and n that intersect at point A.
P
Sketch and label the figures described. Use dashes for hidden lines.
30. Horizontal plane P contains two lines k and n that intersect at point A.
P
KN
A
Sketch and label the figures described. Use dashes for hidden lines.
31. Horizontal plane Q and vertical plane N intersect.
Sketch and label the figures described. Use dashes for hidden lines.
31. Horizontal plane Q and vertical plane N intersect.
Q
N
Sketch and label the figures described. Use dashes for hidden lines.
32. Vertical planes X and Y intersect an .AB�������������� �
YX
Sketch and label the figures described. Use dashes for hidden lines.
32. Vertical planes X and Y intersect an .AB�������������� �
A
B
Sketch and label the figures described. Use dashes for hidden lines.
33. Point P is not in plane N. Three lines through point P intersect N in points A, B, and C.
Sketch and label the figures described. Use dashes for hidden lines.
33. Point P is not in plane N. Three lines through point P intersect N in points A, B, and C.
NA
B C
P
C’est fini.
Good day and good luck.