
Manipulative 1: Perpendicular bisector concurrence.


The Perpendicular Bisector Concurrence Theorem proves that,
for all triangles, the
perpendicular bisectors
of the sides of a triangle are
concurrent
at the
circumcenter
of the
triangle.
If on draws any triangle, then draws the perpendicular bisectors of the sides, all three
perpendicular bisectors will meet at the same point. When three or more lines meet at the
same point, they are said to be concurrent at that point. Furthermore, if one draws a circle
with the center at the point of concurrency and the edge through any of the vertices of the
triangle, it will also pass through the other two vertices. This circle is called the
circumcircle of the triangle. For a proof of the Perpendicular Bisector Concurrence Theorem,
see http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/anderson/finalprojectpart2/finalprojectpart2proof.html.
