give one’s arm to someone—(also: offer one’s arm to someone) allow a person to walk arm-in-arm or lean on one’s arm:
- He turned his back on Alfred, gave his arm to Mrs. Langham and advanced into the hotel.
give one’s hand to someone—(of a woman) agree to marry a man:
- He fails, however, to win Miss Lillerton, who gives her hand to a smooth young curate instead.