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shake hands (with someone)
to clasp and shake the hand of someone as a greeting. His hands were full, and I didn't know whether to try to shake hands with him or not. He put down his packages, and we shook hands.
shake handsand shake someone's hand
to take someone's hand and move it up and down to greet someone or mark an agreement with someone. (See also shake hands (with someone).) David shook my hand when he greeted me. Anne and John shook hands before their business appointment.
1. Also, shake someone's hand. Clasp another's hand in greeting, farewell, or congratulation or as a sign of friendship or goodwill. For example, Stop fighting, boys; shake hands and be done with it, or You won first prize? Let me shake your hand. [Early 1500s]
2. shake hands on. Confirm a promise or bargain, as in We didn't sign a contract; we simply shook hands on our agreement. [Early 1900s]