Axiom 1

Given two points, we can fold a line connecting them

Axiom 2

Given two points, we can fold point 1 onto point 2

Axiom 3

Given two lines, we can fold line 1 onto line 2

Axiom 4

Given a point and a line, we can make a fold perpendicular to the line passing through the point

Axiom 5

Given two points and a line, we can make a fold that places the first point on to the line and passes through the second point

Axiom 6

Given two points and two lines we can make a fold that places the first point onto the first line and the second point onto the second line

oof. this one is hard

Axiom 7

Given a point and two lines we can make a fold perpendicular to the second line that places the point onto the first line