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The centroid is indexed as X(2). Characteristic Property of Centroid at cut-the-knot; Interactive animations showing Centroid of a triangle and Centroid construction with compass and straightedge; Experimentally finding the medians and centroid of a triangle at Dynamic Geometry Sketches, an interactive dynamic geometry sketch using the gravity ...
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object X {\displaystyle X} in n {\displaystyle n} - dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about the hyperplane.
Let A'BC be the equilateral triangle having base BC and vertex A' on the negative side of BC and let AB'C and ABC' be similarly constructed equilateral triangles based on the other two sides of triangle ABC. Then the lines AA', BB', CC' are concurrent and the point of concurrence is the 1st isogonal center. Its trilinear coordinates are
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
These include the Calabi triangle (a triangle with three congruent inscribed squares), [10] the golden triangle and golden gnomon (two isosceles triangles whose sides and base are in the golden ratio), [11] the 80-80-20 triangle appearing in the Langley's Adventitious Angles puzzle, [12] and the 30-30-120 triangle of the triakis triangular tiling.
The incircle itself may be constructed by dropping a perpendicular from the incenter to one of the sides of the triangle and drawing a circle with that segment as its radius. [3] The incenter lies at equal distances from the three line segments forming the sides of the triangle, and also from the three lines containing those segments.
The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at a point called the "vertex centroid" and are all bisected by this point. [10]: p.125
An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. [1] Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered ...