Geometry Postulates

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Author:
mathlover1
ID:
32127
Filename:
Geometry Postulates
Updated:
2010-09-12 17:06:54
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geometry postulates
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Description:
Geometry Postulates...add over time. Based on Euclid's geometry.
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  1. Unique Line Assumption of the Point-Line-Plane Postulate (PLP):
    Dimension Assumption of the PLP:
    Unique Distance Assumption of the PLP:
    • Through any two points, there is exactly one line.
    • point = 0 dimensions; line = 1 dimension; plane = 2 dimensions; space = 3 dimensions
    • On a number line, there is a unique distance between two points. The distance is defined as the absolute value of x-y.
  2. Reflexive Property of Equality:
    Symmetric Property of Equality:
    Transive Property of Equality:
    • a=a
    • If a=b, then b=a
    • If a=b and b=c, then a=c
  3. Addition Property of Equality:
    Multiplication Property of Equality:
    Substitution Property of Equality:
    • If a=b, then a+c=b+c (add the same thing to both sides keeps the problem the same)
    • If a=b, then ac=bc (multiply the same thing to both sides keeps the problem the same)
    • If a=b, then a may be substituted for b in any expression (3x+6=21, x=5, then 3(5)+6=21)
  4. Addition Property of Inequality:
    Multiplication Property of Inequality:
    Equation to Inequality Property:
    Transitive Property of Inequality:
    • If a<b, then a+c<b+c (add the same thing to both sides keeps problem the same)
    • If a<b and c>0, then ac<bc (multiply the same thing to both sides keeps problem the same)
    • If a and b are positive numbers and a+b=c, then c>a and c>b (If a+b=8, then a cannot be greater than 8 when the variables are positive numbers)
    • If a<b and b<c, then a<c
  5. Commutative Property of Addition:
    Commutative Property of Multiplication:
    Distributive Property:
    • a+b=b+a
    • ab=ba
    • a(b+c)=ab+ac
  6. Triange Inequality Postulate:
    The sum of the length of two sides of any triangle is greater than the length of the third side. (a+b>c)
  7. Unique Measure Assumption of the Angle Measure Postulate (AMP):
    Zero Angle Assumption of the AMP:
    Straight Angle Assumption of the AMP:

    (not included: Angle Addition Property of the AMP & the Two Sides of Line Assumption of the AMP)
    • Every angle has a unique measure from 0o to 180o.
    • If ray VA and ray VB are the same ray, then the measure of angle AVB is 0o.
    • If ray VA nad ray VB are opposite rays, the the measure of angle AVB is 180o.
  8. Reflection Postulate (5 parts):
    • Angle measure is preserved.
    • Betweenness is preserved.
    • Collinearity is preserved.
    • Distance is preserved.
    • Each preimage has exactly one image.

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