1. **Problem 13:** If a triangle is acute, then it is an equilateral triangle. - An acute triangle is one where all three angles are less than 90 degrees. - An equilateral triangle has all three angles equal to 60 degrees, which are all acute. - However, not all acute triangles are equilateral; they can be scalene or isosceles with all angles less than 90 degrees but not equal. **Conclusion:** The statement is **sometimes true**. 2. **Problem 14:** If a triangle has two acute angles, it must be an acute triangle. - A triangle has three angles summing to 180 degrees. - If two angles are acute (less than 90 degrees), the third angle could be acute, right (90 degrees), or obtuse (greater than 90 degrees). - For example, if the third angle is obtuse, the triangle is not acute. **Conclusion:** The statement is **sometimes true**. 3. **Problem 15:** An obtuse triangle can have a right angle. - An obtuse triangle has exactly one angle greater than 90 degrees. - A right angle is exactly 90 degrees. - A triangle cannot have both an obtuse angle and a right angle simultaneously because the sum of angles would exceed 180 degrees. **Conclusion:** The statement is **never true**.