<P> Euclid defined an isosceles triangle as one having exactly two equal sides, but modern treatments prefer to define them as having at least two equal sides, making equilateral triangles (with three equal sides) a special case of isosceles triangles . In the equilateral triangle case, since all sides are equal, any side can be called the base, if needed, and the term leg is not generally used . </P> <P> A triangle with exactly two equal sides has exactly one axis of symmetry, which goes through the vertex angle and also goes through the midpoint of the base . Thus the axis of symmetry coincides with (1) the angle bisector of the vertex angle, (2) the median drawn to the base, (3) the altitude drawn from the vertex angle, and (4) the perpendicular bisector of the base . </P> <P> Whether the isosceles triangle is acute, right or obtuse depends on the vertex angle . In Euclidean geometry, the base angles cannot be obtuse (greater than 90 °) or right (equal to 90 °) because their measures would sum to at least 180 °, the total of all angles in any Euclidean triangle . Since a triangle is obtuse or right if and only if one of its angles is obtuse or right, respectively, an isosceles triangle is obtuse, right or acute if and only if its vertex angle is respectively obtuse, right or acute . </P> <P> The Euler line of any triangle goes through the triangle's orthocenter (the intersection of its three altitudes), its centroid (the intersection of its three medians), and its circumcenter (the intersection of the perpendicular bisectors of its three sides, which is also the center of the circumcircle that passes through the three vertices). In an isosceles triangle with exactly two equal sides, the Euler line coincides with the axis of symmetry . This can be seen as follows . Since as pointed out in the previous section the axis of symmetry coincides with an altitude, the intersection of the altitudes, which must lie on that altitude, must therefore lie on the axis of symmetry; since the axis coincides with a median, the intersection of the medians, which must lie on that median, must therefore lie on the axis of symmetry; and since the axis coincides with a perpendicular bisector, the intersection of the perpendicular bisectors, which must lie on that perpendicular bisector, must therefore lie on the axis of symmetry . </P>

Can the base angle of an isosceles triangle be obtuse