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A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted . In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). This article is about triangles in Euclidean geometry except where otherwise noted. ==Types of triangle== ===By lengths of sides=== Triangles can be classified according to the lengths of their sides: *An ''equilateral triangle'' has all sides the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°. *An ''isosceles triangle'' has two sides of equal length.〔Euclid defines isosceles triangles based on the number of equal sides, i.e. ''only two equal sides''. An alternative approach defines isosceles triangles based on shared properties, i.e. ''equilateral triangles are a special case of isosceles triangles''. wikt:Isosceles triangle〕〔 An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with ''at least'' two equal sides. The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles. *A ''scalene triangle'' has all its sides of different lengths. Equivalently, it has all angles of different measure. A right triangle is also a scalene triangle if and only if it is not isosceles. Hatch marks, also called tick marks, are used in diagrams of triangles and other geometric figures to identify sides of equal lengths. A side can be marked with a pattern of "ticks", short line segments in the form of tally marks; two sides have equal lengths if they are both marked with the same pattern. In a triangle, the pattern is usually no more than 3 ticks. An equilateral triangle has the same pattern on all 3 sides, an isosceles triangle has the same pattern on just 2 sides, and a scalene triangle has different patterns on all sides since no sides are equal. Similarly, patterns of 1, 2, or 3 concentric arcs inside the angles are used to indicate equal angles. An equilateral triangle has the same pattern on all 3 angles, an isosceles triangle has the same pattern on just 2 angles, and a scalene triangle has different patterns on all angles since no angles are equal. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). This article is about triangles in Euclidean geometry except where otherwise noted.==Types of triangle==theorem )-->===By lengths of sides===Scalene Triangle -->Triangles can be classified according to the lengths of their sides:*An ''equilateral triangle'' has all sides the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.*An ''isosceles triangle'' has two sides of equal length.Euclid defines isosceles triangles based on the number of equal sides, i.e. ''only two equal sides''. An alternative approach defines isosceles triangles based on shared properties, i.e. ''equilateral triangles are a special case of isosceles triangles''. wikt:Isosceles triangle An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with ''at least'' two equal sides. The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles.*A ''scalene triangle'' has all its sides of different lengths. Equivalently, it has all angles of different measure. A right triangle is also a scalene triangle if and only if it is not isosceles.Hatch marks, also called tick marks, are used in diagrams of triangles and other geometric figures to identify sides of equal lengths. A side can be marked with a pattern of "ticks", short line segments in the form of tally marks; two sides have equal lengths if they are both marked with the same pattern. In a triangle, the pattern is usually no more than 3 ticks. An equilateral triangle has the same pattern on all 3 sides, an isosceles triangle has the same pattern on just 2 sides, and a scalene triangle has different patterns on all sides since no sides are equal. Similarly, patterns of 1, 2, or 3 concentric arcs inside the angles are used to indicate equal angles. An equilateral triangle has the same pattern on all 3 angles, an isosceles triangle has the same pattern on just 2 angles, and a scalene triangle has different patterns on all angles since no angles are equal.」の詳細全文を読む スポンサード リンク
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