# Closed hyperplanes on a normed space are isomorphic

Let $$X$$ be a normed space. I'd like to show that all closed hyperplanes in $$X$$ are isomorphic.

My attempt

Let $$H$$ and $$W$$ be closed hyperplanes. We know $$\dim(X/H)=\dim(X/W)=1$$, therefore $$(X/H)$$ and $$(X/W)$$ are isomorphic. How to conclude that W and H are isomorphic?