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Topic: On a more cheerful note ...
Replies: 4   Last Post: Oct 29, 2011 11:08 PM

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Evan Romer

Posts: 27
From: Conklin Ny
Registered: 2/14/10
On a more cheerful note ...
Posted: Oct 25, 2011 7:26 PM
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One of my colleagues was teaching centroids today, and one of her students wondered if the 6 triangles formed by the medians all had the same area. Interesting. Neither of us had heard of this before, but it seemed plausible.

So I went into GeoGebra and made a triangle with draggable vertices, constructed its medians, found the areas of the six sub-triangles ... and they are all equal no matter what shape I make the big triangle. (GeoGebra file attached. You can drag points A, B and C.)

So it seems true, but can we prove it? ... On and off during the day, together we managed to prove it. Fun day.

Evan Romer
Susquehanna Valley HS
Conklin NY

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