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Proof in Linear Programming - extreme point

Can anyone help me to prove this? I'm really stuck with geometry in Linear Programming...

(See attached file for full problem description and equations)

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Assume P is a polyhedron and H is a supporting hyperplane to P.
Prove that is an extreme point of if and only if is an extreme point of P.

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Question rewritten in available notations:
Assume P is a polyhedron and H is a supporting hyperplane to P.
Prove that N belonging to (P cross H) is an extreme point of (P cross H) if and only if N ...

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