Isosceles Right Triangle

Pronunciation: /aɪˈsɒ.səˌliz raɪt ˈtraɪˌæŋ.gəl/ Explain

Click on the blue points and drag them to change the figure. Manipulative 1 - Isosceles Right Triangle Created with GeoGebra.

An isosceles right triangle is a triangle with one right angle where the measures of the other two angles are equal. Since the sum of the angles of a triangle is 180°, the measure of each of the equal angles is (180° - 90°) ÷ 2 = 45°. Properties of isosceles right triangles One angle of an isosceles right triangle is a right angle. The two base angles of an isosceles right triangle are congruent. The two base angles of an isosceles right triangle both measure 45° = π/4 radians. The two sides of an isosceles right triangle opposite the base angles are congruent. The area of an isosceles right triangle is where b is the length of one of the legs. The perimeter of an isosceles right triangle is where b is the length of one of the legs.

References

1. McAdams, David E.. All Math Words Dictionary, isosceles right triangle. 2nd Classroom edition 20150108-4799968. pg 103. 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. pp 8,19-23. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 8/7/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/8/mode/1up/search/isosceles. Buy the book
3. Sterling, Mary Jane. Trigonometry For Dummies. pg 92. For Dummies. January 28, 2005. Last Accessed 8/7/2018. Buy the book
4. Maekawa, Jun. Genuine Origami: 43 Mathematically-Based Models. pg 21. Japan Publications Trading, November 1. 2008. Last Accessed 8/7/2018. Buy the book

Cite this article as:

McAdams, David E. Isosceles Right Triangle. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/isoscelesrighttriangle.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/23/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
3/3/2010: Added "References", added "Properties of isosceles right triangles". (McAdams, David E.)
8/13/2008: Changed image to GeoGebra manipulative. (McAdams, David E.)
7/11/2007: Initial version. (McAdams, David E.)