Unit 3: Points, Lines, Planes

Euclid

Euclid

~300 B.C., Greek, Father of Geometry, wrote “Elements”, developed bade for all future discoveries of geometry.

5 Postulates

1. two points determine one straight line

2. a straight line extends indefinitely in either direction

3. a circle may be drawn w given center and any radius

4. all right angles are equal

5. given a line k and point p not on the same line, there is only one line m through p that is parallel to k.

Postulate

• “duh” statement

• to assume or claim as true or existent

Theorem

• statements that can be proved

• and HAS been proved

Point

has no actual size, used to rep an object or location in space.

Line

has no thickness or width, reps and continuous set of linear points that extend indefinitely.

Plane

has no thickness width, or depth, used to rep a flat surface that extends in all directions indefinitely.

Euclidean Geometry

not curved, straight.

Non-Euclidian Geometry

Based on curved surfaces like earth or saddle. (hyperbolic and spherical.)

Colinear

set of points that lie on the same line.

Space

set of all points, boundless and 3 dimensional space.

Noncollinear

set of points that do NOT lie on the same line.

Coplanar

points and or lines that lie on the same plane.

NonCoplanar

points and or lines that are not on the same line.

Skew Lines

2 noncoplanar lines that do not intersect.