Ruler with two parallel edges

The constructions with a straightedge alone do not allow much.
Except if we add something else : For instance some device to draw parallel lines etc.
To draw pairs of parallel lines, we may use the two parallel edges of a ruler, with width d.
The "axioms" are then : That's all. However we also allow to choose arbitrary points, if the final result doesn't depend on the exact choice of these points. (for constructions including "draw any line" etc)

By using just these constructions [C1] [C2] [C3] above, to construct :

Can we discard axiom [C3] for these constructions ? Hint

More complicated : to construct an equilateral triangle ? an hexagon ? octogon ? dodecagon ? Hint
A regular pentagon ? decagon ? etc ? Hint
Same question : can we discard axiom [C3] ? Hint

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