1. He shook hands with the person.

2. Tom made friends with Bill.
3. You have to change cars at the intersection.
4. He is on good terms with others.
5. He wanted to exchange seats with Bill.
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Are they all grammatical?

Yes, all are fine.

Nice!

Yes, all of the sentences are grammatically correct. They each demonstrate a different usage of the phrasal verb "to shake hands with," "to make friends with," "to change (something) at," "to be on good terms with," and "to exchange (something) with." Here's a breakdown of each sentence:

1. He shook hands with the person.
This sentence is grammatically correct. "To shake hands with" is a phrasal verb that means to greet someone or say goodbye by clasping their hand with your own.

2. Tom made friends with Bill.
This sentence is also grammatically correct. "To make friends with" is a phrasal verb that means to form a friendship or establish a friendly relationship with someone.

3. You have to change cars at the intersection.
This sentence is grammatically correct. "To change (something) at" is a phrasal verb that means to switch or replace something at a particular location or point.

4. He is on good terms with others.
This sentence is grammatically correct. "To be on good terms with" is a phrasal verb that means to have a positive or friendly relationship with others.

5. He wanted to exchange seats with Bill.
This sentence is grammatically correct. "To exchange (something) with" is a phrasal verb that means to give something and receive something else in return. In this case, it refers to wanting to switch seats with someone, specifically Bill.