Difference between revisions of "Acute triangle"

 
m
Line 4: Line 4:
  
  
The acute triangles can also be defined in different ways:  
+
Acute triangles can also be defined in different ways:  
  
 
* A triangle is acute if and only if each of its [[altitude]]s lies entirely in the triangle's interior.
 
* A triangle is acute if and only if each of its [[altitude]]s lies entirely in the triangle's interior.
  
 
* A triangle with sides of length <math>a, b</math> and <math>c</math> is acute if and only if <math>a^2 + b^2 > c^2</math>, <math>b^2 + c^2 > a^2</math> and <math>c^2 + a^2 > b^2</math>.  This is known as the [[Geometric inequality | Pythagorean Inequality]].
 
* A triangle with sides of length <math>a, b</math> and <math>c</math> is acute if and only if <math>a^2 + b^2 > c^2</math>, <math>b^2 + c^2 > a^2</math> and <math>c^2 + a^2 > b^2</math>.  This is known as the [[Geometric inequality | Pythagorean Inequality]].

Revision as of 21:30, 30 October 2006

This article is a stub. Help us out by expanding it.

An acute triangle is a triangle in which each angle is an acute angle. Any triangle which is not acute is either a right triangle or an obtuse triangle.


Acute triangles can also be defined in different ways:

  • A triangle is acute if and only if each of its altitudes lies entirely in the triangle's interior.
Invalid username
Login to AoPS