A proof establishes the validity of a conjecture for every possible variation of the situation in which it could arise. Initially, students may consider that a demonstration is sufficient.
Watch the video Demonstration of the angle sum of a triangle which provides evidence to conjecture that the angle sum of a triangle is 180°. Students could try this activity for themselves.
In contrast to a demonstration, a geometric proof needs to be an orderly progression of statements which link previously established facts each supported with reasons. Watch the Two Proofs of the Angle Sum of a Triangle slide presentation.
You can also download the accompanying Angle Sum of a Triangle: Student Worksheet.
A dynamic diagram of the angle sum of a triangle is available on Geogebra Tube.
It is important to explain to students that a proof is incorrect if there is:
- an error in the underlying assumptions
- a flaw in the logic of the reasoning.