Interactive Orthopole of a Triangle and a Line. Level: High School, SAT Prep, College

Proposition. Drop perpendiculars AA', BB' and CC' from the vertices of a triangle ABC on any line L. Then the perpendiculars A'A'', B'B'', and C'C'' to the opposite sides of the triangle are concurrent at a point P called the orthopole of triangle ABC and line L.

Click the red button () on the figure to start the animation. Drag points A, C and line L to change the figure. Try the step by step construction.
 

Dynamic Geometry: You can alter the figure dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand.

This page uses the TracenPoche dynamic geometry software and requires Adobe Flash player 7 or higher. TracenPoche is a project of Sesamath, an association of French teachers of mathematics.

Instruction to explore the illustration above:

  • Animation. Click the red button to start/stop animation

  • Manipulate. Drag points A and C, and line AC to change the figure.

  • Step-by-Step construction. Press P and click the left mouse button on any free area to show the step-by-step bar and click 'Next Step' button () to start the construction step-by-step:

     
    Hide the step-by-step bar by using again the combination P + click left mouse.

 

 

 

Triangle Orthopole

 

 

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Last updated: August 1, 2009