## Triangle Altitude construction

An applet to show that the three altitudes of a triangle all meet in a single point.

 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)

The three vertices of the triangle above can each be dragged to show that the three altitudes still meet in a single point when we look at other triangles.

The check box for Extended Altitudes lets you see that this continues to work when the point of intersection is not inside the triangle.

Having verified that the three altitudes meet in a single point, we want to construct a proof.  Select the "Large Triangle" check box.  We see that if we add in three more congruent triangles to the picture, we get a larger triangle.  The altitudes of the original triangle become perpendicular bisectors of the sides of the larger triangle.  Those lines meet in a point that is the center of a circle that circumscribes the larger triangle,

Created with GeoGebra
GeoGebra is a GNUed software package for mathematics visualization.  The home for the applications is  http://www.geogebra.org.