## Thursday, December 16, 2010

### Exterior Angles

"Hey, Mr. Cox.  Is there a theorem that says this?"

I'm not sure.  Why do you think that's true?

"Well if a triangle has 180o and I know two of them, then the third one has to be whatever's left over from 180o.  But that third angle and x make a straight line so they have to add up to 180o too."

If it's true, what would you call it?

"I remember seeing something about 'exterior angle' in the index one time, so that's taken.  Maybe I'll look it up and see what that one means."

*goes and looks up Exterior Angle Theorem*

"Ah, man!  Someone already discovered it."

CalcDave said...

"So, someone discovered the theorem...now can you find some cool uses for it? When would you want to measure an angle, but you can neither measure it nor the supplementary angle?

Sometimes you can get famous by not just discovering a theorem, but finding a lot of (or a few very practical) uses for it."

grace said...

love.

Kris said...

This is great. I'm curious about the when students are getting into these discoveries. Was this during class? If so, what was the class "assignment" at that time.

jgd said...

I'm echoing Kris' comment/question - what was the assignment at the time? How can we set things up so students are playing like this all the time? Got any great hints?

David Cox said...

The question wasn't really part of an assignment at all. This student is working sort of independently as he's already taken algebra as a 7th grader. He's had a lot of autonomy with respect to how we decide to do geometry. He started the year by trying to prove the theorems in the book (his choice) and we've recently started going with a mire problem based approach. This question was all his and it came out if the blue. I suppose it may have been a residual of all of the proofs he'd previously done. (See this one. It's good.