An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos ( leg ).
A triangle with all sides equal is called an equilateral triangle , and a triangle with no sides equal is called a scalene triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal. Another special case of an isosceles triangle is the isosceles right triangle.
The height of the isosceles triangle illustrated above can be found from the Pythagorean theorem as
The inradius of an isosceles triangle is given by
or 2/3 the way from its vertex (Gearhart and Schulz 1990).
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.
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.  The vertex opposite the base is called the apex.
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.
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