22
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
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.
