All 3 Uses

demonstrate
in
Me and Earl and the Dying Girl
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Lunch is where you are asked to demonstrate your allegiance to one group or another by sitting with them for all to see—or, God forbid, being asked to sit with some poor sap who's not even in a group.†
p. 9.4 *

demonstrate = show
There is no evidence that this is true, but he tells everyone about it anyway, and when they ask him for a demonstration, he gets really angry and does the Robot Dance of Anger.†
p. 128.4
I mean, if it does change your mind and you decide to readmit me, then you guys should all be fired, because all I've really demonstrated to you is that I'm a jackass who doesn't feel appropriate emotions and can't really live a normal human life.†
p. 292.6

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)