1. **Problem Statement:** The problem asks about the relationship between the exterior bisector of the vertex angle of an isosceles triangle and its base. 2. **Key Definitions:** - An isosceles triangle has two equal sides and two equal base angles. - The vertex angle is the angle opposite the base. - An exterior bisector of an angle is a ray that divides the exterior angle into two equal parts. 3. **Important Properties:** - In an isosceles triangle, the bisector of the vertex angle is perpendicular to the base. - The exterior bisector of the vertex angle is also perpendicular to the base because it forms a linear pair with the interior bisector. 4. **Explanation:** - The interior bisector of the vertex angle meets the base at a right angle. - The exterior bisector is the extension of the angle bisector outside the triangle. - Since the interior and exterior bisectors form a straight line, the exterior bisector is also perpendicular to the base. 5. **Answer:** The exterior bisector of the vertex angle of an isosceles triangle is **perpendicular** to the base. **Final answer:** (b) perpendicular