To determine the value of m needed to prove that quadrilateral ABCD is a parallelogram, you would typically use properties such as the fact that opposite angles must be equal, or the diagonals must bisect each other, or opposite sides must be equal.
Since I cannot see the image you mentioned for specific details about angles or sides, I will guide you on how to approach the problem:
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If you have angle measurements: Check if any pairs of opposite angles are equal. If they are represented in terms of m, set them equal to each other and solve for m.
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If you have side lengths or expressions involving m: Use the property that opposite sides of a parallelogram are equal. Set the expressions for opposite sides equal to one another and solve for m.
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If you have diagonal lengths: If considering diagonal bisecting properties, set the expressions for the diagonals equal to one another and solve for m.
Once you determine the relationship according to any of the properties mentioned above, the possible values for m must match one of your answers: 36, 15, 11, or 18.
You can substitute each value back into your equations to check which one satisfies the conditions for parallelograms.
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