Both Uses

demonstrate
in
A Raisin in the Sun
(Edited)

(He sits down beside her and demonstrates graphically what he thinks her methods and tone should be)
Scene 1.1

demonstrates = shows
(RUTH folds her hands rather primly on her lap, determined to demonstrate the civilization of the family) Warm, ain't it? I mean for September.
Scene 2.1 *

demonstrate = show

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)