To determine the value of \( m \) that proves that quadrilateral \( ABCD \) is a parallelogram, we typically use the properties of the sides and angles of a parallelogram. For instance, in a parallelogram, opposite sides are equal in length or opposite angles are equal.
Without the specific image or additional information about the sides or angles, I cannot calculate the value of \( m \) directly. However, here are the steps you should consider:
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Check if opposite sides are equal: If you have length expressions for \( AB \) and \( CD \) or \( AD \) and \( BC \), you can set them equal to each other to find \( m \).
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Check if opposite angles are equal: If you have angle measures involving \( m \), set opposite angles equal to find \( m \).
If you provide the relevant equations or relationships shown in the image, I can help you solve for \( m \).
However, if you need a direct answer without the image context, you would typically check each option by substituting it back into your expressions until one fits the condition to prove \( ABCD \) is a parallelogram.