Altitude
Pronunciation: /ˈæl tɪˌtud/ Explain
Abbreviation: alt
Click on the blue points and drag them to change the figure. Click on the check boxes to show the different altitudes.
How do the altitudes change as you change the figure.
 Manipulative 1  Altitude of a Triangle Created with GeoGebra. 

An altitude is the shortest distance from a
vertex
of a geometric figure to a line containing the opposite side (2D) or the base (3D).^{[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
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 an altitude coincide with a leg of the triangle?
 For what type of triangle does an altitude intersect the opposite side?

Click on the blue points and drag them to change the figure.
How does the altitude change as you change the figure?
 Manipulative 2  Altitude of a Cone Created with GeoGebra. 

Click on the blue points and drag them to change the figure.
How does the altitude change as you change the figure.
 Manipulative 3  Altitude of a Cylinder Created with GeoGebra. 

Click on the blue points and drag them to change the figure.
How does the altitude of the pyramid change as you change the figure?
 Manipulative 4  Altitude of a Pyramid Created with GeoGebra. 

References
 Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pg 38. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 8/6/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/38/mode/1up/search/altitude. Buy the book
Cite this article as:
McAdams, David E. Altitude. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/altitude.html.
Image Credits
Revision History
6/13/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (
McAdams, David E.)
12/24/2009: Added reference to Euclid's Elements, Expanded table of angle classes. (
McAdams, David E.)
11/20/2008: Initial version. (
McAdams, David E.)