Concurrence of the Altitudes As Seen from 3D

Stuart Anderson found a proof of the concurrence of altitutdes in a triangle by embedding the triangle into 3D. The applet below serves a dynamic illustration:

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

Created with GeoGebra

The tool bar at the left is fully functional. Selecting the second button from the bottom allows you to rotate the diagram. Also, the vertices of the triangle are draggable such that you can modify the configuration and then view it from a different perspective.

In case GeoGebra does not load, here's a suggestive diagram of how the intersection of the altitudes is seen from 3D:

altitudes from 3D

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