Difference between revisions of "Hypotenuse"

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The '''hypotenuse''' of a [[right triangle]] is the side opposite the [[right angle]]. It is also the longest side of the triangle.
 
The '''hypotenuse''' of a [[right triangle]] is the side opposite the [[right angle]]. It is also the longest side of the triangle.
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The hypotenuse can be found by using the formula
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<math>a^2+b^2=c^2</math> where a and b are legs of the triangle and c is the hypotenuse.
  
 
The hypotenuse is a [[diameter]] of the [[circumcircle]]. It follows that the midpoint of the hypotenuse of the triangle is the center of the circle. The converse also holds: if the length of the median of <math>\triangle ABC</math> from <math>C</math> is the same as <math>\frac12 AB</math>, then <math>\triangle ABC</math> is a right triangle with its right angle at <math>C</math>.
 
The hypotenuse is a [[diameter]] of the [[circumcircle]]. It follows that the midpoint of the hypotenuse of the triangle is the center of the circle. The converse also holds: if the length of the median of <math>\triangle ABC</math> from <math>C</math> is the same as <math>\frac12 AB</math>, then <math>\triangle ABC</math> is a right triangle with its right angle at <math>C</math>.

Revision as of 01:00, 27 February 2010

The hypotenuse of a right triangle is the side opposite the right angle. It is also the longest side of the triangle. The hypotenuse can be found by using the formula $a^2+b^2=c^2$ where a and b are legs of the triangle and c is the hypotenuse.

The hypotenuse is a diameter of the circumcircle. It follows that the midpoint of the hypotenuse of the triangle is the center of the circle. The converse also holds: if the length of the median of $\triangle ABC$ from $C$ is the same as $\frac12 AB$, then $\triangle ABC$ is a right triangle with its right angle at $C$.

See also

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