Final answer:
To prove the isosceles triangle theorem, constructing a perpendicular bisector of the base (Option A) is the best strategy as it creates two congruent right triangles proving opposite angles are equal.
Step-by-step explanation:
The question pertains to the isosceles triangle theorem which states that in an isosceles triangle, the angles opposite the equal sides are also equal. To prove this theorem, the most effective strategy would be Option A: Construct a perpendicular bisector of the base. This construction would split the base into two equal halves and also create two right triangles. Because the sides of the isosceles triangle are of equal length, these two right triangles would be congruent, showing that the angles opposite the equal sides are also equal, thereby proving the theorem.
Measuring angles at the vertices (Option B) would not provide a formal proof, while calculating the area (Option C) or finding the sum of the interior angles (Option D) is not directly related to proving the isosceles triangle theorem.