No.
It need not be the base angles that are equal, it can be one of the base angles and the top angle (if the triangle is tipped over). Also, the base angle are equal in an equilateral triangle - although an equilateral triangle is a special kind of isosceles triangle.
equal
It is an isosceles triangle
An isosceles triangle has three interior angles whose base angles are equal.
The base angles of an isosceles triangle are called the base angles. In an isosceles triangle, two sides are of equal length, and the angles opposite these sides are also equal. This means that the base angles are congruent. The third angle, which is the vertex angle, is located opposite the base.
An isosceles triangle has two equal angles in the base.
The angle that is not congruent to the base angles of an isosceles triangle is called the "vertex angle." In an isosceles triangle, the vertex angle is formed by the two equal sides, while the base angles are the angles opposite the equal sides.
An isosceles triangle has 2 equal sides and 2 equal base angles
The base angles of an isosceles triangle are congruent.
The two base angles are equal
The base angles of an isosceles triangle are the two angles that are equal to each other. They can be between 89.999...o and 0.000000..01o.
An isosceles triangle has 2 equal base angles and its height is perpendicular from its apex to the centre of its base
An isosceles triangle has two equal sides and two equal base angles.