11.1 Basic Notions

Fundamental Building Blocks of Geometry

1. Points

2. Lines

3. Planes (Space)

Def. __Collinear Points__—points on the same line (any 2
points are collinear, but 3 need not be.)

Ex. _{}

Points A, B, C are on _{} and are collinear.

Points A, B, D are not collinear.

Point B is __between__ points A and C on
_{}.

Def. __Line Segment__—a subset of a line that contains
two points of the line and all points between those two points.

Ex. _{}

Def. __Ray__—a subset of a line that
contains the endpoint and all points on the line on one __side__ of the
point.

Ex. _{}

*A plane is determined by three points not on the same line.*

Def. __Coplanar points__—points not placed in a single
plane. (See drawing)

Def. __Noncoplanar____ points__—points
not placed in a single plane. (See
drawing)

Def. __Coplanar lines__—lines in the same plane. (See drawing)

Def. __Skew lines__—lines that do not intersect and there
is not a plane that contains them. (See
drawing)

Def. __Intersecting lines__—two coplanar lines with
exactly one point in common. (See
drawing)

Def. __Concurrent lines__—lines that contain the same
point. (See drawing)

Def. __Parallel lines__—two distinct coplanar lines that
have no points in common.

Ex.

m_{}∕∕ n

Properties of Points, Lines, and Planes

- There
is
__exactly__one line that contains any two distinct points. - If two points lie in a plane, then the line containing the points lie in a plane.
- If two distinct planes intersect, then their intersection is a line.
- There
is
__exactly__one plane that contains any three distinct noncollinear points. - A line and a point not on the line determine a plane.
- Two parallel lines determine a plane.
- Two intersecting lines determine a plane.

Angles

Angle Measurement

Degree—complete rotation is 360°

A __protractor__ is used to measure angles.

Types of angles

- 180°
- 90°
- 0° < angle < 90°
- 90° < angle <180°

Perpendicular lines

When two lines intersect so that the angles formed are right angles, the lines are perpendicular.

Ex. _{}

*If a line and a plane intersect, they can be perpendicular.*

Ex. _{}