An isosceles triangle such as triangle XYZ shown here which I have drawn on the whiteboard is a triangle which 2 congruent sides. The congruent sides in this case XY and XZ are called legs and the third side which is side YZ is called the base. The angles opposite the legs, angles Y and Z are called base angles. I have drew a red arrow showing which ones they are. The angle opposite the base, angle X, is called the vertex angle.
