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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.
Reflexive Property of Equality:
Symmetric Property of Equality:
Transive Property of Equality:
- If a=b, then b=a
- If a=b and b=c, then a=c
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)
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
Commutative Property of Addition:
Commutative Property of Multiplication:
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)
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.
Reflection Postulate (5 parts):
- Angle measure is preserved.
- Betweenness is preserved.
- Collinearity is preserved.
- Distance is preserved.
- Each preimage has exactly one image.