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A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
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.
In geometry, the Lemoine point, Grebe point or symmedian point is the intersection of the three symmedians (medians reflected at the associated angle bisectors) of a triangle. Ross Honsberger called its existence "one of the crown jewels of modern geometry". [1] In the Encyclopedia of Triangle Centers the symmedian point appears as the sixth ...
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
In the diagram, the medians (in black) intersect at the centroid G. Because the symmedians (in red) are isogonal to the medians, the symmedians also intersect at a single point, L . This point is called the triangle's symmedian point , or alternatively the Lemoine point or Grebe point .
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...
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 ...
The Schiffler point of a triangle is the point of concurrence of the Euler lines of four triangles: the triangle in question, and the three triangles that each share two vertices with it and have its incenter as the other vertex. The Napoleon points and generalizations of them are points of concurrency. For example, the first Napoleon point is ...