Both Uses of

demonstrate
in
A Thousand Acres

Those nights he flexed them: he teased me; he charmed his daughters and included them in the game, even allowing them to decide strategy when his play was at a crisis; he topped Jess's stories, and, in some ways, his style of telling them; he sang verses of songs, both familiar and obscure, that were entertaining, but best of all, appropriate, so that you had private realizations, sharp but silly to express, of how everything that was happening at that moment seemed marvelously to fit—that was Pete's gift, and it demonstrated to me an intelligence that I wasn't used to allowing him.†
p. 79.4 *

demonstrated = showed

Every farmer knows a chemical dealer's representative who has taken a demonstration drink of some insecticide—safe as mother's milk, etc. Once, when Verna Clark was still alive and everyone was still using chlordane for corn rootworm, Harold dropped his instructions into the tank and reached in with his hand and picked them out.†
p. 310.9

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