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Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
Suppose that P does not lie on any of the extended sides BC, CA, AB, and let P −1 denote the isogonal conjugate of P. The pedal triangle of P is homothetic to the antipedal triangle of P −1 . The homothetic center (which is a triangle center if and only if P is a triangle center) is the point given in trilinear coordinates by
A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without ...
A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides that are straight relative to the surface . A curvilinear triangle is a shape with three curved sides, for instance, a circular triangle with circular-arc sides. This article is about straight-sided triangles in Euclidean geometry, except where ...
Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given ...
The Gergonne triangle (of ) is defined by the three touchpoints of the incircle on the three sides. The touchpoint opposite A {\displaystyle A} is denoted T A {\displaystyle T_{A}} , etc. This Gergonne triangle, T A T B T C {\displaystyle \triangle T_{A}T_{B}T_{C}} , is also known as the contact triangle or intouch triangle of A B C ...
Also included are the three leading high scorers along with symbols for upperclass point guards, high scoring big men, team scoring averages and point
For any interior point P, the sum of the lengths of the perpendiculars s + t + u equals the height of the equilateral triangle.. Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. [1]