Both Uses

demonstrate
in
Uprising, by Margaret Peterson Haddix
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But he demonstrated as he talked, lifting a shirtwaist from the table, snipping threads, dropping the finished shirtwaist into a basket.†
p. 18.5 *

demonstrated = showed
Oh, be still, my heart.... Bella had heard the other girls talk about going out with boyfriends to dances, or to the movies—she knew what they were saying because they demonstrated bits and pieces of the dance steps, they gestured the scope of a huge movie screen.†
p. 46.1

Definitions:

(1) (demonstrate as in: It demonstrates my point.)
to show
The exact meaning of this sense of demonstrate can depend upon its context. For example:
- "I will demonstrate how to throw a Frisbee." -- show how to do something
- "I will demonstrate how much quicker the new computer is than the old one." -- show how something works
- "Her questioned demonstrated that she was listening and thinking deeply about what was said." -- showed to be true or proved
(2) (demonstrate as in: demonstrate to protest)
a public display supporting a cause -- usually joining with others in a political protest
(3) (meaning too rare to warrant focus)