Properties of Inequalities (Jacobs Geometry)

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Three Possibilities Property
a<b or a=b or a>b
Transitive property of order
if a<b and b<c, then a<c
Addition Property
if a<b then a+c<b+c
Multiplication Property (c is positve)
if a<b then ac<bc
Multiplication Property (c is negative)
if a<b then ac>bc
natural numbers
1,2,3,4,5,6,7....
whole numbers
0,1,2,3,4,5,6,7...
integers
...-3,-2,-1,0,1,2,3...
rational numbers
any number which can be expressed as a ratio of two integers
Subtraction Property
If a > b, then a-c >b-c
Division Property
If a > b and c > 0, then a/c > b/c
"Whole is Great Than its Parts" Property
If c = a + b and b > 0, then c > a
Theorem 18
If two sides of triangle are unequal the angles opposite them are also unequal in the same order
Theorem 19
If two angles of a triangle are unequal the sides opposite them are also unequal in the same order
Triangle Inequality Theorem
The sum of any two angles in triangle is greater than the third side