Search results
Results From The WOW.Com Content Network
Each median divides the area of the triangle in half, hence the name, and hence a triangular object of uniform density would balance on any median. (Any other lines that divide triangle's area into two equal parts do not pass through the centroid.) [2] [3] The three medians divide the triangle into six smaller triangles of equal area.
The median on the hypotenuse of a right triangle divides the triangle into two isosceles triangles, because the median equals one-half the hypotenuse. The medians m a {\displaystyle m_{a}} and m b {\displaystyle m_{b}} from the legs satisfy [ 6 ] : p.136, #3110
In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side.
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle , [ 3 ] a triangle with two sides having the same length is an isosceles triangle , [ 4 ] [ a ] and a triangle with three different-length sides is a scalene triangle . [ 7 ]
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
The median triangle of a given (reference) triangle is a triangle, the sides of which are equal and parallel to the medians of its reference triangle.
In a right triangle, the median from the hypotenuse (that is, the line segment from the midpoint of the hypotenuse to the right-angled vertex) divides the right triangle into two isosceles triangles. This is because the midpoint of the hypotenuse is the center of the circumcircle of the right triangle, and each of the two triangles created by ...
There is only one automedian right triangle, the triangle with side lengths proportional to 1, the square root of 2, and the square root of 3. [2] This triangle is the second triangle in the spiral of Theodorus. It is the only right triangle in which two of the medians are perpendicular to each other. [2]