What is rule to show cause
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One party to a lawsuit has the right to ask the Court to take certain action. Before the Court takes that action, the judge can issue an Order giving another person a time limit within which to come forward and explain why the Court should not take that action.
The topic you selected is "divorce law," so an example from Family Court might help. In a recent case, a father prevented a mother from having contact with their children. The mother filed a petition with the Family Court asking for a Rule to Show Cause why the father should not be held in contempt of Court. If the father fails to come forward, or fails to provide a valid reason, the Court will consider the mother's request solely on the basis of what the mother says happened.