Solution By Steps

Step 1: Identify the statement about an isosceles triangle

The statement provided is: “An isosceles triangle may be right or acute but never obtuse.”

Step 2: Evaluate the truth of the statement

An isosceles triangle is a triangle with at least two sides of equal length. The statement claims that an isosceles triangle can be either right (one angle is 90 degrees) or acute (all angles are less than 90 degrees), but it can never be obtuse (one angle is greater than 90 degrees).

This statement is true because the sum of the angles in a triangle is always 180 degrees. If an isosceles triangle has a right angle (90 degrees), the other two angles must be acute (less than 90 degrees). If an isosceles triangle has all acute angles, the angles must be less than 90 degrees. An isosceles triangle cannot have an obtuse angle because that would make the sum of the angles greater than 180 degrees.

Final Answer

The correct answer is A. True.