Special right triangles are right triangles with additional properties that make calculations involving them easier. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a 2 + b 2 = c 2, where a and b are the lengths of the legs and c is the length of the hypotenuse. The other two sides are called the legs or catheti (singular: cathetus) of the triangle. The side opposite to the right angle is the hypotenuse, the longest side of the triangle.

A right triangle (or right-angled triangle) has one of its interior angles measuring 90° (a right angle).

Triangles can also be classified according to their internal angles, measured here in degrees. 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.

10 Specifying the location of a point in a triangleĮuler diagram of types of triangles, using the definition that isosceles triangles have at least 2 equal sides (i.e., equilateral triangles are isosceles).

9 Figures circumscribed about a triangle.

7.5 Circumcenter, incenter, and orthocenter.

7.1 Medians, angle bisectors, perpendicular side bisectors, and altitudes.

7 Further formulas for general Euclidean triangles.

6.6 Formulas resembling Heron's formula.5.1 Trigonometric ratios in right triangles.

4 Points, lines, and circles associated with a triangle.Isosceles continued to play around Glasgow, with the band supporting Correcto, Clinic, The Vaselines and Shonen Knife. In September of 2008 the band played at the Venice Biennale of Architecture in Venice. Further gigs in England we're followed by appearances at Glastonbury and T In The Park. Alex Kapranos from Franz Ferdinand was at the single launch and asked Isosceles to support them on a tour of the Scottish Highlands including gigs in Inverness, Fort William, Dundee and Portree.Īt the start of 2008 they began their first tour of England before releasing their second single 'Kitch Bitch / Watertight' in April. This exposure resulted in the Leeds based independent record label Art Goes Pop offering to release 'Get Your Hands Off / I Go' in 2007. The band is composed of Jack Valentine, William Aikman, Andrew Wilson and Bobby Duff.įormed in 2006 for a one-off gig, the band began playing gigs around Glasgow and recording songs which would eventually be played by Vic Galloway on Radio One. Isosceles are an indie pop band formed in Glasgow, Scotland. Freebase (0.00 / 0 votes) Rate this definition:

Isosceles triangle definition