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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 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 Nagel point is the isotomic conjugate of the Gergonne point.The Nagel point, the centroid, and the incenter are collinear on a line called the Nagel line.The incenter is the Nagel point of the medial triangle; [2] [3] equivalently, the Nagel point is the incenter of the anticomplementary triangle.
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. The triangle formed by the three parallel lines through the three midpoints of sides of a triangle is called its medial triangle.
The lower half is thin, and ends in a projection called the inferior lateral angle. Medial to this angle is a notch, which is converted into a foramen by the transverse process of the first piece of the coccyx, and this transmits the anterior division of the fifth sacral nerve.
The following result can be used to locate the Spieker center of any triangle. [1] The Spieker center of triangle ABC is the incenter of the medial triangle of ABC. That is, the Spieker center of ABC is the center of the circle inscribed in the medial triangle of ABC. This circle is known as the Spieker circle.
The left lower quadrant (LLQ) of the human abdomen is the area left of the midline and below the umbilicus. The LLQ includes the left iliac fossa and half of the left flank region. The equivalent term for animals is left posterior quadrant. Important organs here are: the descending colon and sigmoid colon; the left ovary and fallopian tube; the ...
The perimeter of the medial triangle equals the semiperimeter of the original triangle, and the area is one quarter of the area of the original triangle. This can be proven by the midpoint theorem of triangles and Heron's formula. The orthocenter of the medial triangle coincides with the circumcenter of the original triangle.