Geometry Notes First Class
Point has zero dimensions

Postulates/Axioms: statement we accept as being true without a proof
Theorems/Corollaries: statement that must be proven before we accept it as being true
Corollaries are spin off of another theorem

Postulates * P1-1 Given any two points, there is a unique distance between them * P1-2 any segment has exactly one midpoint
Theorem
* T1-1 “Midpoint Theorem” If m is the midpoint of segment AB, then: 2AM=AB, AM=1/2AB and 2MB=AB, MB=1/2 AB
Vocab:
Collinear: points that are on the same straight line
Noncollinear Points: Points that are not on same straight line
Obliquely intercept: not at 90 degree angle

Three positions for two lines in space 1. Skew lines: never intercept and not parallel. 2. Parallel Lines: never intercept 3. Intercepting lines: cross each other
Planes
Planes go on forever, never end, like lines.

Line can be: * in plane * Intercept plan * Parallel with plane

Two relationships for Planes 1) Parallel 2) Intercept

Space contains all points

Line with 4 colinear points
Can name it line L, or take two points on the line and same it that way.
AB, AC, AD, BC, BD, with arrows on top.

Subsets of line. * Rays, has only one arrow on top cause starts at point, * Rays going in diff direction on line called opposite rays, same starting points, but opposite directions * Can’t change lettering around with rays cause first letter is starting point. * Line Segment: line that connects two points within the line AB (Gets line on top)

Congruent: equal in measure (the same) ll ll