Relationship between funicular polygon and bending moment diagram

Hello,

I'm a civil engineering student. I found this forum when trying to find some information about the relationship between funicular polygon and bending moment. I don't know if I'm allowed to ask academic questions here...
Well, I'm trying my luck ;p

I learned how to contruct a funicular polygon and bending moment diagrams in two different subjects and I realised how close looking the two are, so I wondered if there was a good explanation to relate the two.

I can feel it's kind of the same as the polygon represents the forces in order for the structure to be in equilibrum and the bending diagram represents how the structure bend in order to stay in equilibrum (is that right ?)

Someone also told me yesterday that the slope of the funicular polygon has something to do with the shear force. I think it's because of the fact that the derivative of the bending moment is the shear force but I'm not sure why.

Thank you in advance for your help and sorry if I'm in the wrong place and also sorry for my bad english.

Melissa