What is the base angle theorem?

The base angle theorem says if two sides of a triangle are congruent, then the angles opposite those sides must also be congruent. The converse is also true. If two angles of a triangle are congruent, then the opposite sides must be also be congruent.

The base angle theorem applies both to isosceles triangles, where two sides are congruent, and to equilateral triangles, where all three sides are congruent. While an equilateral triangle is symmetrical in all three directions, a triangle with only two congruent sides has only one axis of symmetry, which bisects both the noncongruent angle and the noncongruent side and divides the triangle into two congruent right triangles.