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 1/2 b^2 where b is the length of one of the legs.
  • The perimeter of an isosceles right triangle is b*(2+sqrroot(2)) where b is the length of one of the legs.

References

  1. 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 8/6/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/8/mode/1up/search/isosceles. Buy the book
  2. Sterling, Mary Jane. Trigonometry For Dummies. pg 92. For Dummies. January 28, 2005. Last Accessed 8/6/2018. Buy the book
  3. Maekawa, Jun. Genuine Origami: 43 Mathematically-Based 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.)

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