Why? Please
According to the Collins Cobuild Dictionary 6th edition,
A criterion is a factor on which you judge or decide something.
A standard is something that you use in order to judge the quality of something else.
Btw, not a teacher.
Have you looked up the two words in a dictionary?
You assess something against a standard. For example, in a dog show, a the standard for a male in a breed might be "28 cm at the shoulder." A dog that is 28.5 cm or 27.5 would be judged well against the standard. A dog that is on 24 cm would be judged under-sized. (I made that up - I have no idea if height at the shoulder is a normal standard or not.)
A criterion is a yes/no.
You must be at least 25 years old and no more than 40 years old. If you are 24 or 41, you don't meet that criterion.
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