Undefined terms, basic definitions of geometry, postulates, theorems, corollaries and problems based on the theorems.© BrainMass Inc. brainmass.com March 5, 2021, 1:41 am ad1c9bdddf
Basic Geometry (Postulates, theorems and corollaries)
Description: Undefined terms, basic definitions of geometry, postulates, theorems, corollaries and problems based on the theorems.
An axiomatic system has four parts.
Axioms (also called postulates)
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.
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.
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.
Undefined terms, basic definitions of geometry, postulates, theorems, corollaries and problems based on the theorems.