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

1. There is exactly one line that contains any two distinct points.
2. If two points lie in a plane, then the line containing the points lie in a plane.
3. If two distinct planes intersect, then their intersection is a line.
4. There is exactly one plane that contains any three distinct noncollinear points.
5. A line and a point not on the line determine a plane.
6. Two parallel lines determine a plane.
7. Two intersecting lines determine a plane.

Angles

Angle Measurement

Degree—complete rotation is 360°

A protractor is used to measure angles.

Types of angles

1. 180°
2. 90°
3. 0° < angle < 90°
4. 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.