When it has been shown that a conjecture is false, it is sometimes possible to modify the conjecture so it becomes true. Consider the following example.

Example 2

How could the following conjecture be changed to make it true?

Conjecture: A polygon with 3 right angles is a rectangle.

If the polygon is limited to 4 sides, the fourth angle must also be a right angle, which makes a rectangle.

Revised conjecture: A quadrilateral with 3 right angles is a rectangle.

 

For further information about counterexamples of conjectures see pages 18–21 of Principles of Mathematics 11.