Here are the words matched with the correct definitions:

1. **city-state** - an independent state consisting of a city and the area around it
2. **metro** - an underground train system
3. **index** - a system that shows the level of prices and wages, etc. so that they can be compared with those of a previous date
4. **jet lag** - the feeling of tiredness and confusion after you fly between places that have a time difference of several hours
5. **lighthouse** - a tower with a powerful flashing light that guides ships away from danger
6. **factor** - a fact or situation that influences the result of something
7. **overcrowding** - the situation when there are too many people or things in one place
8. **urban sprawl** - the spread of a city into the area surrounding it, often without planning

Let me know if you need help with anything else!