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Lesson Summary. A counterargument is a viewpoint that opposes your main argument. Counterarguments are part of good persuasive writing and speaking strategy, because they show that you've considered other points of view.
A counterexample, in geometry as in other areas of mathematics and logic, is an example that one uses to prove that a particular statement is false. A simple example from primary mathematics uses the statement the inverse of a number is never an integer, and its counterexample would be 1/4.