Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

By the isosceles triangle theorem, the two angles opposite the equal sides are themselves equal, while if the third side is different then the third angle is different.

By the Steiner–Lehmus theorem, every triangle with two angle bisectors of equal length is isosceles.

Terminology

In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.

Euclid defined an isosceles triangle as one having exactly two equal sides, but modern treatments prefer to define them as having at least two equal sides, making equilateral triangles (with three equal sides) a special case of isosceles triangles. In the equilateral triangle case, since all sides are equal, any side can be called the base, if needed, and the term leg is not generally used.

Isosceles (disambiguation)

Isosceles can refer to:

See also

Isosceles (band)

Isosceles are an indie pop band formed in Glasgow, Scotland. The band is composed of Jack Valentine (Guitar & Vocals), William Aikman (Keyboards & Vocals), Andrew Wilson (Bass) and Bobby Duff (Drums).

Formed 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. This exposure resulted in the Leeds based independent record label Art Goes Pop offering to release "Get Your Hands Off / I Go" in 2007. 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.

At the start of 2008 they began their first tour of England before releasing their second single "Kitch Bitch / Watertight" in April. Further gigs in England we're followed by appearances at Glastonbury and T In The Park. In September of 2008 the band played at the Venice Biennale of Architecture in Venice. Isosceles continued to play around Glasgow, with the band supporting Correcto, Clinic, The Vaselines and Shonen Knife.