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In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) 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 special case.
d(x, z) ≤ max {d(x, y), d(y, z)} (strong triangle inequality or ultrametric inequality). An ultrametric space is a pair ( M , d ) consisting of a set M together with an ultrametric d on M , which is called the space's associated distance function (also called a metric ).
A golden triangle. The ratio a/b is the golden ratio φ. The vertex angle is =.Base angles are 72° each. Golden gnomon, having side lengths 1, 1, and .. A golden triangle, also called a sublime triangle, [1] is an isosceles triangle in which the duplicated side is in the golden ratio to the base side:
An equilateral triangle base and three equal isosceles triangle sides It gives 6 isometries, corresponding to the 6 isometries of the base. As permutations of the vertices, these 6 isometries are the identity 1, (123), (132), (12), (13) and (23), forming the symmetry group C 3v , isomorphic to the symmetric group , S 3 .
An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. [1] Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered ...
In an acute isosceles triangle, it is possible to draw a similar but smaller triangle, one of whose sides is the base of the original triangle.The gnomon of these two similar triangles is the triangle remaining when the smaller of the two similar isosceles triangles is removed from the larger one.
The unique 6-point isosceles set in the plane. The shaded regions show four of the 20 isosceles triangles formed by triples of these points. In discrete geometry, an isosceles set is a set of points with the property that every three of them form an isosceles triangle.
For example, the dual of a highly acute isosceles triangle is an obtuse isosceles triangle. In the Dorman Luke construction , each face of a dual polyhedron is the dual polygon of the corresponding vertex figure .