Sunday, 29 May 2011

Neat Geometry

Just came across a nice geometric idea from Antonio Gutierrez. Not surprising since he has been posting nice geometry on the internet for quite a while.   If you teach geometry, or have a kid who wants to learn geometry, this ought to be on your reader list. 
So for this one, take any scalene triangle and pick a point on the same plane... any point.. go on, I'll wait. 

OK, Ready?  Now draw  a segment from the point to any vertex.  I chose A above in Red.

Now draw a perpendicular to that segment through your point. Also draw the extension of the side of the triangle opposite the vertex you chose to connect (in my case, segment BC).   Finally mark the point where the perpendicular you created passes the opposite side. 

Now do that with the other two vertices.  What happens?  Turns out the three intersections all lie on the same line. 

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