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In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect at the triangle's centroid .
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]
The three perpendicular bisectors meet at the circumcenter. Other sets of lines associated with a triangle are concurrent as well. For example: Any median (which is necessarily a bisector of the triangle's area) is concurrent with two other area bisectors each of which is parallel to a side. [1]
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.
A perpendicular bisector of a side of a triangle is a straight line passing through the midpoint of the side and being perpendicular to it, forming a right angle with it. [19] The three perpendicular bisectors meet in a single point, the triangle's circumcenter ; this point is the center of the circumcircle , the circle passing through all ...
An anatomical plane is a hypothetical plane used to transect the body, in order to describe the location of structures or the direction of movements.. In human anatomy and non-human anatomy, four principal planes are used: the median plane, sagittal plane, coronal plane, and transverse plane.
The parameters in a triangle inequality can be the side lengths, the semiperimeter, the angle measures, the values of trigonometric functions of those angles, the area of the triangle, the medians of the sides, the altitudes, the lengths of the internal angle bisectors from each angle to the opposite side, the perpendicular bisectors of the ...
In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. [1] [2] Medians and angle bisectors are special cases of cevians. The name "cevian" comes from the Italian mathematician Giovanni Ceva, who proved a well-known theorem about cevians which also bears his name. [3]