There are a couple things at work here. One is
the structure of the molecule cellulose.
Cellulose is a very long molecule and
is almost woven together in the wall (see this
image for a cross section:
plant cell wall
This gives it a lot of what's called tensile
strength: it is strongest when it is being
So for example, a string has tensile strength when
you are pulling on either end, or a balloon has
tensile strength the more water you put in it and
the more it stretches out. The most important
aspect of the cell wall remaining rigid is
actually exactly like that. Plant cells get
stuffed full of water to keep the cellulose in the
walls tight. This makes them rigid, and is also
why plants that haven't been watered will lose
their stiffness and droop.
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