\( \triangle A B C \) and \( \triangle D B C \) lie on the same side of \( B C \), as shown in t...

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\( \triangle A B C \) and \( \triangle D B C \) lie on the same side of \( B C \), as shown in the figure. From a point \( P \) on \( B C, P Q \| A B \) and \( P R \| B D \) are drawn, meeting \( A C \) at \( Q \) and \( C D \) at \( R \) respectively. Prove that \( Q R \| A D \).
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