An applet to show that the three perpendicular bisectors of the sides of a triangle all meet in a single point.
The three vertices of the triangle above can each be dragged to show that the perpendicular bisectors of the three sides still meet in a single point when we look at other triangles
When a mathematician sees a behavior like this that works with all
triangles
(or at least with a bunch of examples that we have looked at) the
suspicion is that there must be a structure that helps us prove that it
must always happen.
The check boxes in the diagram
provide the framework for the proof. Click the box labeled "Prelim
Circle". From any point on a perpendicular
bisector, we can construct a circle centered at that point, going
through the two vertices that form the end of the segment. Moving down
the bisector we
reach a point where the circle goes through all three vertices. That
point must be on all three perpendicular bisectors. We can see
that circle directly with the box marked "Final Circle".
Created with GeoGebra
GeoGebra is a GNUed software package for mathematics visualization.
The home for the applications is http://www.geogebra.org.
Return to the GeoGebra Applet page.
Return to the Applets for courses below calculus page.
Return to the Calculus Applet page.
Return to the Saint Louis University Department of Mathematics and Computer Science home page
Last updated By Mike May, S.J., August 12, 2007.