12/17/12
A
Given : BF and CF lie in plane m
AF!FB, AF!FC
Pr ove : AF!m
m
F
C
B
G
E
C
Q
A
B
P
m
D
F
H
A, B, C, D, P, and Q are coplanar points.
!##"
!##"
AB and CD are coplanar lines.
AB and CD are coplanar segments.
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12/17/12
G
E
C
Q
A
B
P
m
D
F
H
A, B, C, D, P, and E are not coplanar points.
!##" !##"
!#"
AB, CD, and EF are not coplanar lines.
AB, CD and EF are not coplanar segments.
G
E
C
Q
A
B
P
m
D
F
H
The point of intersection of a line and a plane is called the foot of the
line.
P is the foot of EF in plane m.
Q is the foot of GH in plane m.
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12/17/12
Three noncollinear points determine a plane.
A line and a point not on it determine a plane.
Two intersecting lines determine a plane.
Two parallel lines determine a plane.
If a line intersects a plane, the intersection is exactly one point.
If two planes intersect, the intersection is exactly one line.
A
Given : Plane m
!ABC " !ABD
m
BD " BC
Pr ove : AD " AC
D
B
C
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12/17/12
A line is perpendicular to a plane if it is perpendicular to every line in the
plane at its foot.
If a line is perpendicular to 2 distinct lines through its foot, then the line is
perpendicular to the plane.
4