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Definition

AB means |a-b|

Definition

An acute angle is an angle whose measure is less than 90 degrees.

Definition

An angle is two rays that have a common endpoint.

Definition

H is between G and I iff GH + HI = GI (p21)

Definition

A set of points is collinear iff they lie on the same line

2 or more lines are concurrent iff they all share a common point

The contrapositive of an If-then statement interchanges the If part with the Then part AND negates both parts.


The contrapositive of P->Q is not-Q->not-P

The converse of an If-then statement interchanges the If part with the Then part.


The converse of If P, then Q is If Q, then P.
The converse of P->Q is Q->P

Definition

A line segment (segment)AB is the points A and B together with all points D such that A-D-B

Idea

An if-then statement and its contrapositive must either both be true or both be false. They are said to be logically equivalent.

Point M is the midpoint of AB iff AM=MB and A-M-B.

Definition

(ray)AB and (ray)AC are opposite rays iff A is between B and C, or iff B-A-C.

One and only 1 line can be drawn through any two points.


Or


Two points determine a line.

Postulate

You can match up every real number with a point on the line.


OR


There is a 1-1 correspondence between the points on a line and the real numbers so that every point matches up with a single real number and every real number matches up with a single point


OR


There exists a function whose domain is the points on a line and whose codomain is the real numbers such that no two points on the line are mapped to the same real number and every element in the codomain is the image of some point in the domain.

Postulate

You can match up every angle with a number between 0 and 180.


OR


Every angle has a unique measurement which is some number between 0 and 180 degrees inclusive.

Definition

Ray (ray)MP is the set of all points C such that M-C-P or M-P-C.

If P is the midpoint of line segement TF, then PF = (1/2) TF

Theorem

On any line L, there are 5 different points on L. If we have a line L, there are 5 different points on L.

Definition

Triangle ABC is defined as non-collinear points A, B and C and the line segments (s)AB, (s)BC, (s)CA

The vertices of tri ABC are A, B and C. They are the "corners" of the triangle. The singular of vertices is vertex.