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Language & Basis of Geometry

Language & Basis of Geometry

Author: Rachel Kaplan
Description:

To understand:
-points
-lines
-planes
-axioms/postulates
-theorems

In this learning packet, we will define the basic terms used in geometry and provide examples.

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Tutorial

Point, Line, and Plane

Axioms/Postulates

Examples of Postulates

	Postulates

A)  Through any two points, there is exactly one line.

B) Dimension Assumption: Given a line in a plane, there exists a point in the plane not on that line. 
C) If two points lie on a plane, the line containing them also lies on the plane.

D) Through three noncolinear points, there is exactly one plane.

E) If two different planes have a point in common, then their intersection is a line.
F) A line segment can be extended indefinitely along a line.
 

Theorems

Examples of Theorems

Theorems

A) Two different lines intersect in at most one point. 
B) If C is between A and B and on segment AB, then AC + CB = AB.
Related Theorems:
C) If A, B, and C are distinct points and AC + CB = AB, then C lies on segment AB.

D) Pythagorean Theorem: a2 + b2 = c2, if c is the hypotenuse.
 

Note: While you can usually get away with not knowing the names of theorems, your Geometry teacher will generally require you to know them.