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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]
The basic triangle on a unit sphere. Both vertices and angles at the vertices of a triangle are denoted by the same upper case letters A, B, and C. Sides are denoted by lower-case letters: a, b, and c. The sphere has a radius of 1, and so the side lengths and lower case angles are equivalent (see arc length).
The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height. A graphic derivation of the formula T = h 2 b {\displaystyle T={\frac {h}{2}}b} that avoids the usual procedure of doubling the area of the triangle and then halving it.
A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS). For all cases in the plane, at least one of the side lengths must be specified. If only the angles are given, the side lengths cannot be determined, because any similar triangle is a solution.
A hyperbolic triangle embedded in a saddle-shaped surface. In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane.It consists of three line segments called sides or edges and three points called angles or vertices.
The area (A) of a regular heptagon of side length a is given by: A = 7 4 a 2 cot π 7 ≃ 3.634 a 2 . {\displaystyle A={\frac {7}{4}}a^{2}\cot {\frac {\pi }{7}}\simeq 3.634a^{2}.} 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 ...
Let a triangle be given with vertices A, B, and C, opposite sides of lengths a, b, and c, area K, and a line that is tangent to the triangle's incircle at any point on that circle. Denote the signed perpendicular distances of the vertices from the line as a ', b ', and c ', with a distance being negative if and only if the vertex is on the ...
A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . Letting be the semiperimeter of the triangle, = (+ +), the area is [1]