11.1 Basic Notions

 

Fundamental Building Blocks of Geometry

 

1.      Points

2.      Lines

3.      Planes (Space)

 

Def. Collinear Points用oints 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預 subset of a line that contains two points of the line and all points between those two points.

Ex.

 

Def. Ray預 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用oints not placed in a single plane. (See drawing)

 

Def. Noncoplanar points用oints not placed in a single plane. (See drawing)

 

Def. Coplanar lines様ines in the same plane. (See drawing)

 

Def. Skew lines様ines that do not intersect and there is not a plane that contains them. (See drawing)

 

Def. Intersecting lines葉wo coplanar lines with exactly one point in common. (See drawing)

 

Def. Concurrent lines様ines that contain the same point. (See drawing)

 

Def. Parallel lines葉wo 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幼omplete rotation is 360ー

 

 

 

 

 

 

 

A protractor is used to measure angles.

 

 

Types of angles

 

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

 

 

 

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.