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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.
A convex equilateral pentagon can be described by two consecutive angles, which together determine the other angles. However, equilateral pentagons, and equilateral polygons with more than five sides, can also be concave, and if concave pentagons are allowed then two angles are no longer sufficient to determine the shape of the pentagon.
Definition of 1 radian. Throughout history, angles have been measured in various units. ... It is the angle of the equilateral triangle or is ...
A triangle in which one of the angles is a right angle is a right triangle, a triangle in which all of its angles are less than that angle is an acute triangle, and a triangle in which one of it angles is greater than that angle is an obtuse triangle. [8] These definitions date back at least to Euclid. [9]
It can be shown that two triangles having congruent angles (equiangular triangles) are similar, that is, the corresponding sides can be proved to be proportional. This is known as the AAA similarity theorem. [2] Note that the "AAA" is a mnemonic: each one of the three A's refers to an "angle".
An alternated hexagon, h{6}, is an equilateral triangle, {3}. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. A regular hexagon can be dissected into six equilateral triangles by adding a center point. This pattern repeats within the regular triangular tiling.
The equilateral triangle, with three 60° angles, is acute. The Morley triangle, formed from any triangle by the intersections of its adjacent angle trisectors, is equilateral and hence acute. The golden triangle is the isosceles triangle in which the ratio of the duplicated side to the base side equals the golden ratio. It is acute, with ...
A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law).