Search results
Results from the WOW.Com Content Network
Pasch's axiom — Let A, B, C be three points that do not lie on a line and let a be a line in the plane ABC which does not meet any of the points A, B, C.If the line a passes through a point of the segment AB, it also passes through a point of the segment AC, or through a point of segment BC.
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 ...
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 .
The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at a point called the "vertex centroid" and are all bisected by this point. [ 10 ] : p.125 The four "maltitudes" of a convex quadrilateral are the perpendiculars to a side through the midpoint of the opposite side, hence bisecting the latter side.
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
The three splitters concur at the Nagel point of the triangle. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter, and each triangle has one, two, or three of these lines. [2] Thus if there are three of them, they concur at the incenter.
the intersection points of a constructed circle and a constructed segment, or line through a constructed segment, or; the intersection points of two distinct constructed circles. As an example, the midpoint of constructed segment is a constructible point. One construction for it is to construct two circles with as radius, and the line through ...
The full axiom system proposed has point, line, and line containing point as primitive notions: Two points are contained in just one line. For any line L and any point P, not on L, there is just one line containing P and not containing any point of L. This line is said to be parallel to L. Every line contains at least two points.