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Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.
In geometry, the midpoint polygon of a polygon P is the polygon whose vertices are the midpoints of the edges of P. [1] [2] It is sometimes called the Kasner polygon after Edward Kasner, who termed it the inscribed polygon "for brevity". [3] [4] The medial triangle The Varignon parallelogram
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 red triangle is the medial triangle of the black. The endpoints of the red triangle coincide with the midpoints of the black triangle. In Euclidean geometry, the medial triangle or midpoint triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC, BC.
In Euclidean geometry, Varignon's theorem holds that the midpoints of the sides of an arbitrary quadrilateral form a parallelogram, called the Varignon parallelogram. It is named after Pierre Varignon , whose proof was published posthumously in 1731.
The midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine-point circle. [27] The remaining three points for which it is named are the midpoints of the portion of altitude between the vertices and the orthocenter. The radius of the nine-point circle is half that of the circumcircle.
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a compass.
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