glacier

A dome is a large rounded roof or ceiling, so being rounded is essential to a dome. A geodesic dome (choice b) is only one type of dome. Some, but not all domes, have copper roofs (choice d). Domes are often found on government buildings (choice c), but domes exist in many other places.

A saddle is something one uses to sit on an animal, so it must have a seat (choice b). A saddle is often used on a horse (choice a), but it may be used on other animals. Stirrups (choice c) are often found on a saddle but may not be used. A horn (choice d) is found on Western saddles, but not English saddles, so it is not the essential element here.

Without a first-place win, there is no champion, so winning is essential. There may be champions in running, swimming, or speaking, but there are also champions in many other areas.

A cage is meant to keep something surrounded, so enclosure is the essential element. A prisoner (choice b) or an animal (choice c) are two things that may be kept in cages, among many other things. A zoo (choice d) is only one place that has cages.

Without a signature, there is no autograph. Athletes and actors (choices a and b) may sign autographs, but they are not essential. An autograph can be signed with something other than a pen (choice d).

A directory is a listing of names or things, so (choice b) is the essential element. A telephone (choice a) often has a directory associated with it, but it is not essential. A computer (choice c) uses a directory format to list files, but it is not required.Names (choice d) are often listed in a directory, but many other things are listed in directories, so this is not the essential element.

An agreement is necessary to have a contract. A contract may appear on a document (choice b), but it is not required. A contract may be oral as well as written, so choice c is not essential. A contract can be made without an attorney (choice d).

A hurricane cannot exist without wind. A beach is not essential to a hurricane (choice a). A hurricane is a type of cyclone, which rules out (choice b). Not all hurricanes cause damage (choice c).

Residents must be present in order to have a town. A town may be too small to have skyscrapers (choice b). A town may or may not have parks (choice c) and libraries (choice d), so they are not the essential elements.

Something cannot vibrate without creating motion, so motion is essential to vibration.