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Teachers' Lounge Discussion: Coordinate proofs

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From: Bill Crawford

To: Teacher2Teacher Public Discussion
Date: 2007062216:45:02
Subject: Re: Coordinate proofs

	
Heron's Formula is a bit like magic to many beginning geometry
students. I like to ask the class to find the area using (1/2)bh. Of
course, they will have to determine the "height" given the base. By
finding the equation of the line perpendicular to any side which
passes through the opposite vertex, the student can find the point of
intersection of the two lines and the distance from that point to the
vertex. Try dividing the class into three groups and have them each
determine a separate altitude. If you use an obtuse triangle then one
group will find an altitude that intersects the extension of a side.
Finally, by graphing the triangle and each altitude the students will
find the circumcenter. Now ask them to find the coordinates of this
point of concurrency and to calculate the distance from the point to
each vertex. This is a wonderful exercise that will allow the students
to practice a number of skills. 

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