Relating lines to planesLesson 6.1

Dedicated To Graham Millerwise

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 plane4 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 points - many planes

n

1.

Theorem 45: A line and a point not on the line determine a plane.

2.

Theorem 46: Two intersecting lines determine a plane.

3.

4. Theorem 47: Two parallel lines determine a plane.

Two postulates concerning lines and planes

Postulate 1: If a line intersects a plane not containing it, then the intersection is exactly one point.

X

C

Y

m

Postulate 2: If two planes intersect, their intersection is exactly one line.

m

n

1. m Ո n = ___2. A, B, and V determine plane ___3. Name the foot of RS in m.4. AB and RS determine plane ____.5. AB and point ______ determine plane n.6. Does W line in plane n?7. Line AB and line ____ determine plane

m.8. A, B, V, and _______ are coplanar

points.9. A, B, V, and ______ are noncoplanar

points.

ABm

P

R or S

nR or S

NoVW

W or P

A

P

BC

m

Given: ABC lie in plane m

PB AB

PB BC

AB BC

Prove: <APB <CPB

1. PB AB, PB BC2. PBA & PBC are rt

s3. PBA PBC4. AB BC5. PB PB6. ΔPBA ΔPBC7. APB CPB

1. Given2. lines form rt s3. Rt s are 4. Given5. Reflexive Property6. SAS (4, 3, 5)7. CPCTC