What type of roof is characterized by a rigid form with two pitches or slopes?

The correct answer is the gambrel roof. This type of roof is distinguished by its two distinct slopes on each side. The lower slope is steeper than the upper slope, typically creating a barn-style look that is often associated with agricultural buildings, although it can also be seen on residential properties. The design allows for more living space in the upper levels of a building, making it both functional and aesthetically appealing.

In contrast, a flat roof has little to no pitch, which does not align with the definition in the question. The mansard roof is similar in having two slopes but does not have the same specific form as the gambrel, as it usually features a single steep lower slope and a more gradual upper slope. Lastly, a hip roof has slopes on all four sides that converge at the top, rather than the two-sided configuration of a gambrel roof. Understanding these distinctions helps clarify why the gambrel roof is the correct answer to the question.