A question about a YouTube video on Thales's Theorem

[murshid_islam]

TL;DR

Is this Thales's Theorem or the converse of Thales's Theorem?

Here is the video in question:

In the video at 4:23, Michael says, "Now Thales's Theorem tells us that the two other points, where these rays contact the circumference, are diametrically opposed. They are on opposite sides of the circle and a line passing through them will pass through the centre."

Isn't that the converse of Thales's Theorem? Yes, the converse is true as well, but what was stated in the video isn't Thales's theorem; it's the converse as far as I understand. Am I missing something?

 

[.Scott]

You are correct - it is the converse and, in this case, the converse is also true.

That said, it is a combination of Thales's Theorem and other logic that would tell us that those two points are diametrically opposed. So his statement "Thales's Theorem tells us that the two other points, where these rays contact the circumference, are diametrically opposed" is arguably correct or arguably incomplete.

Since the title of his Video is "Thales's Theorem", he should probably have been more precise.

 

[mfb]

It's a relatively trivial consequence of the theorem, or even part of the theorem if you prefer that view. There is no authority that would define what exactly is part of a theorem and what is not.*

*even though I had a professor thinking they would be that authority