Geometry June 25, 2008 1st Qtr

Undefined Terms

> no formal definition
> described or represented
> dealt with through their properties which are taken up as postulates

1) Point
> no dimension
> represented by a dot
> named by a capital letter

2) Line
> set of points extending infinitely in both directions
> length but no width or thickness
> arrowheads
> named using 2 points at each end or a small letter at one end or in the middle

Types of Lines:
2.1) Line Segment
> set of points in between 2 points
> named by endpoints
2.2) Ray
> one endpoint and extends indefinitely in one direction
> named by two points
2.3) Opposite Rays
> 2 rays with a common endpoint contained on the same line going in opposite directions
2.4) Half Lines
> union of all points of a line on one side of a point excluding the point

3) Plane
> infinite length and width but no thickness
> flat surface
> represented by 4-sided figures
> named by 3 non collinear points or capital letter on the corner

POSTULATES
>assumed to be true
> statements accepted with proof

THEOREMS
> statements that can be
proven using preceding terms, definitions, postulates, and possibly previously proven theorems

SPACE: Set of all Points

Congruent Segments:
> same length

Collinear
> same line

Non collinear
> not same line

Coplanar
> same plane
>within the plane

Non coplanar
> not same plane
> outside the plane

MIDPOINT
Divide a segment into 2 congruent parts

BETWEENESS

H-E-Y --> HE+EY=HY

BISECTOR
> midpoint of a segment; line, half line, ray, segment, plane passing through the midpoint