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Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle , [ 3 ] a triangle with two sides having the same length is an isosceles triangle , [ 4 ] [ a ] and a triangle with three different-length sides is a scalene triangle . [ 7 ]
Emile Lemoine (1840–1912) In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed roughly since the beginning of the last quarter of the nineteenth century. Triangles and their properties were the subject of investigation since at least the ...
The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura (1903-1983). The problem asks for the largest number N (k) of nonoverlapping triangles whose sides lie on an arrangement of k lines. Variations of the problem consider the projective plane rather than the Euclidean plane, and require that ...
60°. An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.
If all the triangles are equilateral, the symmetry can also be distinguished by colouring the 8 and 12 triangle sets differently. Pyritohedral symmetry has the symbol (3*2), [3 + ,4], with order 24. Tetrahedral symmetry has the symbol (332), [3,3] + , with order 12.
The diagonals cut the quadrilateral into four triangles of which one opposite pair have equal areas. [16]: Prop.5 The product of the areas of the two triangles formed by one diagonal equals the product of the areas of the two triangles formed by the other diagonal. [16]: Thm.6
convex, cyclic. Dual polygon. Self-dual. In geometry, an isosceles triangle (/ aɪˈsɒsəliːz /) is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a ...
Sum of angles of a triangle. In a Euclidean space, the sum of angles of a triangle equals a straight angle (180 degrees, π radians, two right angles, or a half- turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. It was unknown for a long time whether other geometries exist, for which this sum is different.
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