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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 ...
File:Equilateral triangle with height square root of 3.svg. Add languages. ... A 30-60-90 triangle embedded in an equilateral triangle with sides of length 2.
If a, b and c each cannot be negative, P is restricted to the triangle bounded by A, B and C, as in (2). In (3), the axes are rotated to give an isometric view. The triangle, viewed face-on, appears equilateral. In (4), the distances of P from lines BC, AC and AB are denoted by a′, b′ and c′, respectively.
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Given the edge length .The surface area of a truncated tetrahedron is the sum of 4 regular hexagons and 4 equilateral triangles' area, and its volume is: [2] =, =.. The dihedral angle of a truncated tetrahedron between triangle-to-hexagon is approximately 109.47°, and that between adjacent hexagonal faces is approximately 70.53°.
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]
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.
A polyhedron with only equilateral triangles as faces is called a deltahedron. There are only eight different convex deltahedra, one of which is the regular icosahedron. [4] The regular icosahedron can also be constructed starting from a regular octahedron. All triangular faces of a regular octahedron are breaking, twisting at a certain angle ...
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