What is the key characteristic of an isosceles triangle?

An isosceles triangle is defined by having two sides that are equal in length, which is the key characteristic that distinguishes it from other types of triangles. This property leads to several important implications: the angles opposite the equal sides are also equal, creating a symmetrical shape. This symmetry can be visualized if you were to draw a line from the apex (where the two equal sides meet) down to the base; this line bisects the triangle into two congruent right triangles.

The ability of an isosceles triangle to maintain equal lengths for two sides allows for specific geometric reasoning and can also lead to insights in trigonometry and other mathematical applications. It is important to note that while some triangles may have all sides equal (equilateral) or contain a right angle, these characteristics do not define an isosceles triangle, underlining the exclusivity of the two-sides-equal property.