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\(PQ\) and \(RS\) are two equal and parallel line-segments. Any point \(M\) not lying on \(PQ\) or \(RS\) is joined to \(Q\) and \(S\) and lines through \(P\) parallel to \(QM\) and through \(R\) parallel to \(SM\) meet at \(N\). Prove that line segments \(MN\) and \(PQ\) are equal and parallel to each other.
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