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These points are all on the Euler line . A midsegment (or midline) of a triangle is a line segment that joins the midpoints of two sides of the triangle. It is parallel to the third side and has a length equal to one half of that third side. The medial triangle of a given triangle has vertices at the midpoints of the given triangle's sides ...
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both ...
Midpoint theorem (triangle) The midpoint theorem or midline theorem states that if the midpoints of two sides of a triangle are connected, then the resulting line segment will be parallel to the third side and have half of its length. The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are ...
Median (geometry) 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 centroid.
Construction of an arbitrary bisected line segment on a given line. Given a line, m (in black), and a circle centered at A, we wish to create points E, B, and H on the line such that B is the midpoint: Draw an arbitrary line (in red) passing through the given circle's center, A, and the desired midpoint B (chosen arbitrarily) on the line m.
Constructions in hyperbolic geometry. Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate, is changed. The fifth axiom of hyperbolic geometry says that given a line L and a point P not on that line, there are at least two lines passing through P ...
Bottema's theorem is a theorem in plane geometry by the Dutch mathematician Oene Bottema ( Groningen, 1901–1992). [1] The theorem can be stated as follows: in any given triangle , construct squares on any two adjacent sides, for example and . The midpoint of the line segment that connects the vertices of the squares opposite the common vertex ...
The area enclosed by a parabola and a line segment, the so-called "parabola segment", ... The point B is the midpoint of the line segment FC. Deductions