Definition:Triangle (Geometry)/Isosceles
Definition
An isosceles triangle is a triangle in which two sides are the same length.
Base
The base of an isosceles triangle is specifically defined to be the side which is a different length from the other two.
In the above diagram, $BC$ is the base.
Base Angles
The two (equal) vertices adjacent to the base of an isosceles triangle are called the base angles.
In the above diagram, $\angle ABC$ and $\angle ACB$ are the base angles.
Apex
The vertex opposite the base of an isosceles triangle is called the apex of the triangle.
In the above diagram, $A$ is the apex.
Legs
The sides of an isosceles triangle which are adjacent to the apex are called the legs of the triangle.
In the above diagram, $AB$ and $AC$ are the legs.
Also defined as
Some sources require that in an isosceles triangle, the third side has to be specifically of a different length than the two defined as being equal.
Hence, under such a definition, an equilateral triangle would not be classified as isosceles.
Euclid's Definition
In the words of Euclid:
- Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.
(The Elements: Book $\text{I}$: Definition $20$)
Also see
- Results about isosceles triangles can be found here.
Linguistic Note
The word isosceles comes from the Greek: $\iota \sigma \omicron \sigma \kappa \epsilon \lambda \epsilon \varsigma$, that is: from iso meaning equal, and skelos meaning leg.
Thus an isosceles triangle is literally an equal-leg triangle.
It is pronounced eye-sos-ell-eez, that is, with the emphasis on the second syllable. Note that the c is silent.
The word skeleton comes from the same linguistic root.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): triangle (Euclidean geometry)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): isosceles triangle
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): triangle
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): isosceles triangle
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): triangle
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): isosceles triangle