Level 155
Level 157

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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.