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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.
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]
The area (A) of a regular heptagon of side length a is given by: = . This can be seen by subdividing the unit-sided heptagon into seven triangular "pie slices" with vertices at the center and at the heptagon's vertices, and then halving each triangle using the apothem as the common side.
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]
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
Move alpha, beta, gamma in front of height lines: 18:14, 4 August 2012: 192 × 168 (28 KB) MartinThoma: added background: ... Equilateral triangle; Usage on ta ...
Additionally, among the curves of constant width, the Reuleaux triangle is the one with both the largest and the smallest inscribed equilateral triangles. [15] The largest equilateral triangle inscribed in a Reuleaux triangle is the one connecting its three corners, and the smallest one is the one connecting the three midpoints of its sides ...
The dihedral angle between two adjacent square faces is the internal angle of an equilateral triangle π /3 = 60°, and that between a square and a triangle is π /2 = 90°. [7] The volume of any prism is the product of the area of the base and the distance between the two bases. [8]
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