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The triangle medians and the centroid.. 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 cent
The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). [6] The centroid divides each of the medians in the ratio 2 : 1 , {\displaystyle 2:1,} which is to say it is located 1 3 {\displaystyle {\tfrac {1}{3}}} of the distance from each side to the opposite ...
In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors: A triangle's altitudes run from each vertex and meet the opposite side at a right angle. The point where the three altitudes meet is the orthocenter.
The three medians intersect in a single point, the triangle's centroid or geometric barycenter. The centroid of a rigid triangular object (cut out of a thin sheet of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field. [30]
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.
The three medians of a triangle intersect at the triangle's centroid (the point on which the triangle would balance if it were made of a thin sheet of uniform-density metal). The nine-point center of a triangle lies at the midpoint between the circumcenter and the orthocenter. These points are all on the Euler line.
A reference triangle's medial triangle is congruent to the triangle whose vertices are the midpoints between the reference triangle's orthocenter and its vertices. [2]: p.103, #206, p.108, #1 The incenter of a triangle lies in its medial triangle. [3]: p.233, Lemma 1 A point in the interior of a triangle is the center of an inellipse of the ...
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.