3-Dimentional Geometry

Points that lie on the same line.

PLANE – A flat surface that extends in all directions without end and no thickness.

A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC).

A

D B

C plane

Any three or more points that lie in the same plane.

Two non-coplanar lines that never intersect.

PARALLEL PLANES – two or more planes that never intersect.

Ex)__________________________________________The floor and the ceiling of a room.

PERPENDICULAR PLANES – two planes that intersect at right angles.

Ex)__________________________________________The floor and a wall of a room.

Note: Two planes are perpendicular to each other if and only if ______________________________________________one plane contains a line perpendicular to the second plane

Two Points define a Line

Two Lines intersect at a Point

Two Intersecting Lines define a Plane

Two planes intersect at a line

A B

A

Three Non Collinear Points define a Plane

A line is perpendicular to a plane when it extends directly away from it, like a pencil standing up on a table

If the pencil is perpendicular to a line on the table, then it might be perpendicular to the table

Or it might be leaning over

But if it is perpendicular to two lines (where they intersect) then it will be perpendicular to the table:

When a line is perpendicular to two lines on the plane (where they intersect), it will be perpendicular to the plane.

It will also be perpendicular to all lines on the plane that intersect there.

THEOREMS:1. Given a point there passes one and only one line perpendicular to a given plane.

2. Converse: Given a point there passes one and only one plane perpendicular to a given line.

3. If a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane

4. Two lines perpendicular to the same plane are coplanar

5. If two planes are perpendicular to the same line, they are parallel

6. If a plane intersects two parallel planes, then the intersection is two parallel lines

Parallel Planes!!

True or False?

FALSE

FALSETRUE

TRUE

FALSE

f. At a given point on a given line, only one line is perpendicular to the line ___________________

FALSE