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°. Click on the blue points in
manipulative 1 and drag them to change the manipulative.
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
 Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pp 8,1923. 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/8/mode/1up/search/isosceles. Buy the book
 Sterling, Mary Jane. Trigonometry For Dummies. pg 92. For Dummies. January 28, 2005. Last Accessed 8/6/2018. Buy the book
 Maekawa, Jun. Genuine Origami: 43 MathematicallyBased Models. pg 21. Japan Publications Trading, November 1. 2008. Last Accessed 8/6/2018. Buy the book
Cite this article as:
McAdams, David E. Isosceles Right Triangle. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/isoscelesrighttriangle.html.
Image Credits
Revision History
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.)