Co p lanar Points
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Transcript of Co p lanar Points
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Coplanar Points
C
D
BA
P
DCBA
Collinear Points are points on the same line.
are points that lie in the same plane.
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D
C
B
A
Non-collinear points
are points that do not lie on 1 line.
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H
G
FE
D
CB
A
Non-coplanar points
are points that do not lieOn 1 plane.
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Point A is on line 1.
L1
A
Point A is in line 1.
Line 1 contains point A.
Line 1 is through point A.
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L2L1
A
The intersection of line 1 and line2 is point A.
Intersection means the elements in both sets.
Is the symbol for intersection.
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Which is in? L2
L1
Which is thru?
L1
L2
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In? Under? Above?
L3
L2
L1
L1 L2L3
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Which plane containsPoint A ?Point B ?Point C ?Point D ?Line AB ?
DC
B
A
H
V
Both
Both
Both
HV
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Classroom Ex. P. 7 1-10Y
X
W
ST
O
R
M
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Classroom Ex. P. 7 11-20
D C
HB
A
G
FE
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Complete ShapesHow many planes are drawn?
Add Lines to complete the diagram.
How many planes are drawn?6
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Complete 3-D diagrams
Number of Planes = 7
Number of Planes = 8
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Name the segment that go through point V.
V
T
SR
WName the rest of thePlanes.
VRS
VWTVWR
VST
RST
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V
T
SR
W
Complete the
pyramid.
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Alternative Plane Drawings
F
ED
CB
A
Note that the intersection of two planes is a line.
AD�������������� �
Therefore, segment AD stretches out to be a line.A real planes goes on for ever.
The boundaries of the planes are only in the model.
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G
A
B
C
DE
F
Name the back plane.
Name the left plane.
Name the bottom plane.
Name the top plane.
Name the front plane.
BCF
CDE
ABC
ABG
ADE
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H
RL
B
AA
B
A
A
Three planes can intersect at a 1 line.
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G
A
B
C
DE
F
Three planes can intersect at a 1 point.
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G
FE
D
C
H
RL
B
AA
B
A
A
Point C is in plane _____
Point D is in plane _____
Point E is in plane _____
Point F is in plane _____
Point G is in plane _____
Point A is in plane _____
Point B is in plane _____
H
R
L
H
L
L, R, H
L, R, H
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MS
W
O
T
R
Y
X
XY�������������� �
True or False
Intersects plane M at point O.
True
#1
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Plane M intersects at more than 1 point.
MS
W
O
T
R
Y
X
XY�������������� �
True or False
False
#2
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MS
W
O
T
R
Y
XTrue or False
T, O and R are collinear.
False
#3
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MS
W
O
T
R
Y
XTrue or False
X, O, and Y are collinear.
True
#4
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MS
W
O
T
R
Y
XTrue or False
R, O, S, and W are coplanar.
True
#5
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MS
W
O
T
R
Y
XTrue or False
R, S, T, and X are coplanar.
False
#6
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MS
W
O
T
R
Y
XTrue or False
R, X, O and Y are coplanar.
True
#7
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MS
W
O
T
R
Y
X
Does a plane have edges?
No
#8
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MS
W
O
T
R
Y
X
Can a given point be in 2 lines? Ten lines?
Yes
#9
Yes
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MS
W
O
T
R
Y
X
Can a given line be in 2 planes? In 10 planes?
Yes
#10
Yes
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Find the fourth point of the plane.
A, B, C, ___
False
#11-16
H G
FE
D C
BA
B, G, C, ___B, E, F, ___A, D, E, ___
D, C, H, ___E, F, H, ___D G G
H A F
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H G
FE
D C
BA
Are there any points in line CG besides C and G?
Are there more than 4 points in plane ABCD?
Yes
Yes
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H G
FE
D C
BA
Name the intersection of plane ABFE and BCGF.
Name two planes that do not intersect.
BF�������������� �
ABCD & DFGH ABFE & DCGH ADHE & BCGF
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C’est fini.
The End