Review outline 1

Foundations

Undefined terms
- point
- line
- lie on
Theory
- I1 every pair of distinct points lie on a unique line
- I2 every line has at least two points
- I3 there exist three points that are non-colinear
Example models
Defined terms
- intersect
- parallel
- colinear
Sample theorems / propositions

Undefined terms
- point
- line
- lie on
- distance
- angle measure
N1 (EP) there are at least two points
N2 (IP) two points determine a line
N3 (RP) every line admits a coordinate function f such that |f(P)-f(Q)|=PQ
Defined terms
- coordinate function
- between
- ray
- segment
- congruence of segments
- convex
Theorems
- Betweenness can be expressed in terms of coordinates
- Ruler placement
- Point construction

N4 (PS) for every line l, the points not on l can be partitioned into two convex sets H1 and H2 such that if P is in H1 and Q is in H2 then the segment PQ meets l.
Defined terms
- two sides of a line
- on the same side
- on opposite sides
- angle
- interior of an angle
- betweenness for rays
Theorems
- betweenness for points versus betweenness for rays
N5 (PP) every angle has a measurement in [0,180); an angle measure of 0 means the two rays of the angle are the same; given any ray and angle measurement, there is a unique angle on each side of the ray with the given measurement; the measures of adjacent angles add up to the measure of the larger angle
Defined terms
- congruence of angles
- acute angle
- right angle
- obtuse angle
Theorems
- betweenness theorem for rays
- crossbar theorem
- linear pair theorem
- vertical angles theorem
N6 (SAS) if AB is congruent to DE, angle ABC is congruent to DEF, and CD is conrguent to EF, then triangle ABC is congruent to DEF.
Defined terms
- triangle
- isosceles triangle
- congruence of triangles
Theorems
- isosceles triangle theorem