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In geometry, symmedians are three particular lines associated with every triangle.They are constructed by taking a median of the triangle (a line connecting a vertex with the midpoint of the opposite side), and reflecting the line over the corresponding angle bisector (the line through the same vertex that divides the angle there in half).
Any line perpendicular to any chord of a circle and passing through its midpoint also passes through the circle's center. The butterfly theorem states that, if M is the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly, then M is the midpoint of XY.
A symmetry of the projective plane with a given conic relates every point or pole to a line called its polar. The concept of centre in projective geometry uses this relation. The following assertions are from G. B. Halsted. [3] The harmonic conjugate of a point at infinity with respect to the end points of a finite sect is the 'centre' of that ...
To draw the parallel (h) to a diameter g through any given point P. Chose auxiliary point C anywhere on the straight line through B and P outside of BP. (Steiner) In the branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions imposed on the traditional rules.
Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection. In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit ...
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A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .
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