Altitude

Pronunciation: /ˈæl tɪˌtud/ ?
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Manipulative 1: Altitude. Created with GeoGebra.

An altitude is the shortest distance from a vertex of a geometric figure to a line containing the opposite side (2-D) or the base (3-D).[1] The altitude is always perpendicular to the opposite side. The foot of an altitude is the point where the altitude intersects the line containing the opposite side.

Manipulative 1 shows the altitudes of a triangle. Click on the blue points and drag them to change the figure. The red lines are the altitudes. The dotted lines are the lines which contain the opposite side. The feet of the altitude are the purple dots. Click on the GeoGebra reset button reset button to return the manipulative to its original configuration.

Discovery

  • For what type of triangle is the foot of an altitude not on the leg of the triangle?
  • For what type of triangle does the altitude coincide with a leg of the triangle?
  • For what type of triangle does the altitude intersect the opposite side?
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Manipulative 2: Altitude of a cone. Created with GeoGebra.
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Manipulative 3: Altitude of a cylinder. Created with GeoGebra.
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Manipulative 4: Altitude of a pyramid. Created with GeoGebra.

References

  1. altitude. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=altitude&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, pg 38. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/38/mode/1up/search/altitude.

Cite this article as:


Altitude. 2009-12-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/altitude.html.

Translations

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Revision History


2009-12-24: Added reference to Euclid's Elements, Expanded table of angle classes. (McAdams, David.)
2008-11-20: Initial version (McAdams, David.)

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