Before attempting this proof, students must know that angles in a triangle add to \(180^\circ.\) They must also know how to perform basic algebra. Specifically, they will need to combine like terms and factor.
Our first goal for students is to have them make the conjecture. Have students begin by opening this file in Geogebra:
Tell them they are allowed to move point \(C\) anywhere along the arc \(AB.\) Ask them what they notice. Alternatively, you could give them a sheet of various triangles in semicircles and a protractor. The conjecture students make may be wrong, but either way, have them attempt to prove it. If they fail to make a conjecture, nudge them along by telling them to concentrate on angle \(ACB.\)
After students have found a proof of Thales's theorem, with or without your help, have them open this Geogebra file:
This is nice because it lets students verify the claim for any angle they like. It bolsters their confidence in the theorem and the validity of their proof. Doing so isn't strictly necessary, but I think it makes the experience more enjoyable.