Perpendicular Bisector Concurrence Theorem

Pronunciation: /ˌpɜr pənˈdɪk yə lər ˈbaɪ sɛk tər kənˈkɜr əns ˈθɪər əm/ Explain

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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.

References

1. Durell, Clement V.. A Concise Geometry. pg 97. www.archive.org. G. Bell and Sons, Ltd.. 1921. Last Accessed 8/15/2010. http://www.archive.org/stream/concisegeometry032982mbp#page/n105/mode/1up. Buy the book