Warm Up. 6.1 Relating lines to planes Obj: understand basic concepts to planes Identify four methods of determining a plane Apply two postulates concerning.

Warm Up

6.1 Relating lines to planes

Obj: understand basic concepts to planesIdentify four methods of determining a planeApply two postulates concerning lines and planes

Obj: understand basic concepts to planesIdentify four methods of determining a planeApply two postulates concerning lines and planes

Plane

Two dimensions (length and width)

No thickness Does not end or

have edges Labeled with lower

case letter in one corner

Two dimensions (length and width)

No thickness Does not end or

have edges Labeled with lower

case letter in one corner

m

Coplanar

Points, lines or segments that lie on a plane

Points, lines or segments that lie on a plane

Non-CoplanarPoints, lines or segments that do not lie in the same plane

A

B

Cm

A

C

B

m

Definition:

Point of intersection of a line and a plane is called the foot of the line.

B is the foot of AC in the plane m.A

C

B

m

4 ways to determine a plane

Three non-collinear points determine a plane

One point - many planes

Two points - one line or many planes

Three linear point - many planes

1. n

n

T45: A line and a point not on the line determine a plane.

2.

T46: Two intersecting lines determine a plane.

3.

4.

T47: Two parallel lines determine a plane.

Two postulates concerning lines and planes

P1: If a line intersects a plane not containing it, then the intersection is exactly one point.

X

C

Y

m

P2: If two planes intersect, their intersection is exactly one line.

m

n