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I have two guestions.

1. I would like to know which is correct.
a. Recently I encountered a cab driver who was warm and friendly, helping me with books and parcels.
b. Recently I encountered a cab driver who was warm and friendly, helped me with books and parcels.

2. If "a" is correct, I wonder if "helping" is a present participle or a gerund.
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a. is correct. A gerund, by definition, is a form of a verb used as a noun. So this is simply the present participle.
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WowenglishI wonder if "1" and "2" have the same meaning.
1. Recently I encountered a cab driver helping me with books and parcels.

2. Recently I encountered a cab driver who helped me with books and parcels.
No! What you need, if you want the same meaning, are these:

Recently I encountered a cab driver helping me with books and parcels.
Recently I encountered a cab driver who was helping me with books and parcels.

Both are equally nonsense, but they mean the same thing. Emotion: smile
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You cannot be both the person who encountered someone and the person who was already engaging in some activity with the person you encountered!

CJ
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Comments  
I wonder if "1" and "2" have the same meaning.

1. Recently I encountered a cab driver helping me with books and parcels.

2. Recently I encountered a cab driver who helped me with books and parcels.
#2 is the sentence you want. #1 makes it sound as though all of a sudden you came across a driver and he was in the process of helping you with your books.
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 CalifJim's reply was promoted to an answer.