Final answer:
The best first step to indirectly prove that the base angles of an obtuse isosceles triangle are acute is to assume that they are not acute (choice D), which will lead to a contradiction and thereby show that base angles must indeed be acute.
Step-by-step explanation:
To prove indirectly that the base angles of an obtuse isosceles triangle must be acute, the best first step is to assume that the base angles are not acute. This assumption is represented by choice D: Assume that the base angles are not acute. By making this assumption, we can demonstrate that it leads to a contradiction, which therefore proves that the base angles must be acute.
Remember that in an isosceles triangle, the base angles are equal. Since a triangle's angles must sum up to 180 degrees, and the triangle is given as obtuse (meaning one angle is greater than 90 degrees), the other two angles must be acute to ensure the sum does not exceed 180 degrees.
If we mistakenly assume that the base angles are obtuse or right angles, we would immediately find a contradiction, as it would be impossible for all angles to fit the criteria of a triangle's angles summing to 180 degrees.