Plagiarism is the use of another writer's words or ideas, or information from another source, without giving proper credit.
Properly citing a source's words, ideas, or facts amounts to borrowing from that source. Plagiarism, by contrast, is stealing; trying to pass another person's thinking or writing off as your own.
Why Does This Matter?
Plagiarism can have serious consequences. It is a form of dishonesty; a person that plagiarizes is lying by claiming that another person's work is their own.
Getting caught plagiarizing can get you in a lot of trouble. If it happens when you are in school, you could fail the assignment or even the class. If it happens when you are a professional working in your field, you could lose your job, and your reputation could be badly damaged.
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Words vs Ideas
There are two kinds of plagiarism.
Taking another person's words without giving credit is the more obvious one. Any time you use another person's exact words in your own writing, you need to put quotes around the passage you are borrowing to let the reader know that these words belong to someone else. You also need to give credit by citing the source, letting the reader know where you got those words.
Taking another person's ideas without giving credit. This is less obvious but still plagiarism. Any time when you are writing that you use an idea, argument, concept, opinion, or other idea that you found in another person's writing, you need to give credit, even if you summarized or paraphrased in your own words. You can give credit by adding a citation to show the reader where the idea originally came from.