Pasch's axiom, intermediate value theorem and Jordan curve theorem

Question

All of these three conclusions seem "obvious" to laypeople, and they appear to be somehow connected. I am wondering whether Pasch's axiom can be viewed as a corollary of intermediate value theorem (IVT) and/or Jordan curve theorem (JCT) with appropriate settings. However, I have failed to deduce Pasch's axiom from IVT and/or JCT without further recourse to even less obvious "axioms", which makes me speculate that Pasch's axiom is indeed much more "fundamenetal" than IVT and/or JCT.

Answer 1

For the IVT, as stated in the comments:

Suppose line $\ell$ intersects side $AB$ of $\triangle ABC$. (In other words, line $\ell$ intersects line $AB$ at a point $X$ such that $X$ is between $A$ and $B$.)

Then $A$ and $B$ are on different sides of $\ell$. (This is commonly defined exactly as above: the intersection point of $AB$ with $\ell$ lies between $A$ and $B$.)

By the IVT, the curve that goes from $A$ to $B$ by following segment $AC$ then segment $CB$ must also intersect $\ell$, which is exactly Pasch's axiom.