The right triangle is labeled " orthogonius", and the two angles shown are "acutus" and "angulus obtusus". The first page of Euclid's Elements, from the world's first printed version (1482), showing the "definitions" section of Book I. Equivalently, it has all angles of different measure. A scalene triangle ( Greek: σκαληνὸν, romanized: skalinón, lit.'unequal') has all its sides of different lengths.The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles. The latter definition would make all equilateral triangles isosceles triangles. 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. This fact is the content of the isosceles triangle theorem, which was known by Euclid. An isosceles triangle also has two angles of the same measure, namely the angles opposite to the two sides of the same length. An isosceles triangle ( Greek: ἰσοσκελὲς, romanized: isoskelés, lit.'equal legs') has two sides of equal length.An equilateral triangle is also a regular polygon with all angles measuring 60°. An equilateral triangle ( Greek: ἰσόπλευρον, romanized: isópleuron, lit.'equal sides') has three sides of the same length.The names used for modern classification are either a direct transliteration of Euclid's Greek or their Latin translations.Īncient Greek mathematician Euclid defined three types of triangle according to the lengths of their sides: The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of Euclid's Elements. Euler diagram of types of triangles, using the definition that isosceles triangles have at least 2 equal sides (i.e., equilateral triangles are isosceles).
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