Definition:Triangle (Geometry)/Isosceles

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Definition

An isosceles triangle is a triangle in which two sides are the same length.

IsoscelesTriangle.png


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.


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.