# Basic postulates, and theorems

Undefined terms, basic definitions of geometry, postulates, theorems, corollaries and problems based on the theorems.

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Basic Geometry (Postulates, theorems and corollaries)

Description: Undefined terms, basic definitions of geometry, postulates, theorems, corollaries and problems based on the theorems.

Introduction

An axiomatic system has four parts.

Undefined terms

Axioms (also called postulates)

Definitions

Theorems

Undefined Term

Definition

An undefined term is a term or word that doesn't require further explanation or description.

There are four undefined terms. They are set, point, line and plane.

Let's describe all four undefined terms.

Set: A group or collection with common characteristics.

Examples

A set of points on a line.

A set of all odd integers.

A set of all red flowers.

Point: A point is a tiny dot. It has no dimensions (length, width, height). It is usually denoted by a capital letter.

Line: The term "line" means a straight line. A line is an unlimited number of points along the same path. The line extends indefinitely in both directions. It is represented by a drawn line with arrowheads on each end to represent that it doesn't have endpoints. If it has end points, then it is called a line segment or segment.

A line can be named in two ways:

1. Use the capital letters representing two points on the line and place a double-headed arrow above the two letters. ((AB) ⃡)

2. Use a lowercase letter beside the line to represent it.

Plane: A flat surface that extends indefinitely in all directions.

Axioms

There are 8 axioms which deal the relationship between points and lines, points and planes, lines and planes, and distance and location.

Each axiom is denoted by a capital letter A.

Let's discuss the axioms one by one.

A1. Given any two distinct points, there is exactly one line that contains them.

It gives a relationship between the undefined terms, point and line.

A2. (The Distance Postulate) To every pair of distinct points there corresponds a unique positive number. This number is called the distance between the two points.

The distance between two points, A and B, is denoted by AB. It means the distance from A to B.

This ...

#### Solution Summary

Undefined terms, basic definitions of geometry, postulates, theorems, corollaries and problems based on the theorems.