1. The problem asks to identify the type of triangle given that sides AB and AC are equal, both labeled with length $x$. 2. In geometry, a triangle with two equal sides is called an isosceles triangle. 3. Since AB = AC, the triangle ABC is isosceles. 4. The equal sides imply that the angles opposite those sides are also equal, so $m\angle B = m\angle C$. 5. Therefore, the triangle is an isosceles triangle by definition.