How the check works
The furniture is treated as a box. Whatever goes through a doorway has one side pointing through the opening and the other two across it: one must fit the door's clear width, the other its clear height. The checker tries the piece upright, on its back and on its side, then tilted in the frame, and with the legs off if you tick that box. With a hallway, it also works out the longest piece of that width that can be carried round a right-angled corner.
Measuring a sofa's diagonal depth
Sofas are not boxes: the seat sits lower than the back, so a sofa tipped onto its back can be narrower than its depth or height. Lay a straight edge from the top of the back to the front of the arm, then measure from the bottom of the back up to the straight edge at right angles. If that is less than the door's clear width, the sofa can usually be tilted back through.
Measure the clear opening, not the door: open the door fully and measure from the face of the door to the stop on the other side, at the narrowest point. Check handles, hinges and skirting that stick out, and allow for blankets or wrapping.