Counterexample — Geometry, what it means and where it is taught
A single case that makes a claim false. One is enough.
Taught in Geometry.
Where it is taught
Practise this idea
3 questions in the course bank use Counterexample, in Definitions, Postulates & Reasoning, How to Write a Proof.
Problem 1
"Through any two points there is exactly one line" is a
- postulate
- theorem
- definition
- counterexample
Worked answer
postulate
It is assumed without proof.
That makes it a postulate.
Problem 2
How many counterexamples are needed to disprove a claim?
Worked answer
1
One case that fails makes the claim false.
Proving needs every case; disproving needs one.
Problem 3
Give a counterexample to "all quadrilaterals with four equal sides are squares".
Worked answer
a rhombus
A rhombus has four equal sides.
Its angles need not be right angles.