How do I work out from viewing my shared matches on AncestryDNA which one of my parents is the parent of my half sibling?
You need to find a known relative on your mother's or father's side that has also done an AncestryDNA test. That relative will presumably match your father or mother. If they also match the half sibling then that indicates which one is their parent. It is not proof because there could be other reasons for the matches. For proof you would need to test your father and your mother.