From: Bill Crawford
To: Teacher2Teacher Public Discussion
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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