Difference between revisions of "Hypotenuse"
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By the [[Pythagorean theorem]], the length of the hypotenuse of a triangle with legs of length <math>a</math> and <math>b</math> is <math>\sqrt{a^2 + b^2}</math>. | By the [[Pythagorean theorem]], the length of the hypotenuse of a triangle with legs of length <math>a</math> and <math>b</math> is <math>\sqrt{a^2 + b^2}</math>. | ||
| − | For any right triangle, 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>. | + | For any right triangle, 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>. |
==See also== | ==See also== | ||
Latest revision as of 18:02, 15 October 2018
The hypotenuse of a right triangle is the side opposite the right angle. It is also the longest side of the triangle.
By the Pythagorean theorem, the length of the hypotenuse of a triangle with legs of length 
and 
is 
.
For any right triangle, 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 
from 
is the same as 
, then is a right triangle with its right angle at .
See also
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