Final answer:
A triangle with two sides serving as altitudes must be right-angled (right triangle), since the two altitudes form a right angle with the remaining sides.
Step-by-step explanation:
When a triangle has 2 sides that also serve as altitudes, it means that those two sides are perpendicular to the other sides of the triangle. Since altitudes are perpendicular lines from a vertex to the opposite side (or the line containing the opposite side), having two sides that are altitudes means that they are perpendicular to the other two sides. This configuration necessarily forms a right angle where the altitudes intersect. Thus, such a triangle must be right-angled (or a right triangle), and the correct answer is D) Right-angled.
The sides of a right triangle can be related using the Pythagorean theorem, which states that for a right triangle with legs a and b, and hypotenuse c, the relationship is a² + b² = c². In this context, the two altitudes can be considered as the legs, and the third side as the hypotenuse of the right triangle.