Geometry Reasongs Essay, Research Paper

GEOMETRY REASONS

Points, Lines, Planes, and Angles

Space is the set of all points.

Collinear points are points all in one line.

Coplanar points are points all in one plane.

The intersection of two figures is the set of points that are in both figures.

Statements that are accepted without proof are called postulates or axioms.

Ruler Postulate

1.Any two desired points can have coordinates 0 and 1.

2. The distance between any tow points equals the absolute value of the difference of their coordinates.

Segment Addition Postulate

If B is between A and C, then

AB + BC = AC.

Congruent segments are segments that have equal lengths.

The midpoint of a segment is the point that divides the segment into two congruent segments.

A bisector of a segment is a line, segment, ray, or plane that intersects the segment at its midpoint.

An angle is a figure formed by two rays that have the same endpoint. The two rays are called the sides of the angle, and their common endpoint is the vertex of the angle.

Protractor Postulate

On AB in a given plane, choose any point O between A and B. Consider