# 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 (2-D) or the base (3-D).[2] 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

1. McAdams, David E.. All Math Words Dictionary, altitude. 2nd Classroom edition 20150108-4799968. pg 13. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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 6/12/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/38/mode/1up/search/altitude. Buy the book

McAdams, David E. Altitude. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/altitude.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)