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The word property can have several meanings:
Property is something that belongs to someone. If someone buys a car, the car becomes their property. The Statue of Liberty is the property of the people of the United States. People who deal with buying or selling houses will often talk about "properties", meaning houses, apartments, offices etc.
Properties can also mean the things that make something interesting: the things that give it its characteristics. For example: "Elasticity is a property of rubber", in other words: rubber is elastic. This is close to the meaning for chemistry (see below).
In chemistry, properties refer to the things that describe a material. For example, water is liquid under normal conditions, boils at 100 degrees, is colourless, is odorless, and so on. All these descriptions are properties of water.
In the theatre properties are things which are used in the performance of a plays or opera. Anything that is used but is not part of the scenery (the set) is a property (or "prop" for short), e.g. furniture, a tree, a book that an actor pretends to read, a pipe that they smoke. The props are looked after by a properties master. Sometimes, for small things like books or fans, it is the actor who is responsible for making sure he has the prop. This is called a "personal prop".