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Level 156

Axioms & Postulates III


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Axiom 1
if equals are added to equals their sums are equal
axiom 2
if equals are subtracted from equals their differences are equal
axiom 3
if equals are multiplied to equals their products are equal
axiom 4
if equals are divided by nonzero equals their quotients are equal
axiom 5
(reflective law) a quantity is = to itself.
axiom 6
(symmetric law) is a=b then b=a, if a+b=y then y=a+b
axiom 7
(transitivity law) is a=b, and b=c, then a=c
axiom 8
a=y and a=x then x=y, if a=x, b=y, and a=b then x=y, if a=b, and a+x=y, then b+x=y
postulate 1
once around a circle is 360 degrees
postulate 2
only one line can be between 2 points
postulate 3
2 lines can only intersect once
postulate 4
a line segment is the shortest distance between 2 point on a plane
Postulate 5
any geometric shape can be moved without it changing its form
Postulate 6
a line segment can only have 1 mid point
postulate 7
an angle can only have 1 bisector
postulate 8
the perpendicular is the shortest line segment between a point and a line
postulate 9
the sum (of the measures) of the angles on one side of the line is 180 degrees
postulate 10
2 adjacent angles are supplementary IF their exterior sides are in a straight line
Axiom 1
Every line consists of infinitely many points (is a set of infinitely many points).
axiom 2
Through any two distinct points there is exactly one line.