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Find the value of v that makes quadrilateral CDEF a parallelogram.

Find the value of v that makes quadrilateral CDEF a parallelogram.-example-1

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The value of v that makes CDEF a parallelogram is 2. This is found by setting the lengths of opposite sides equal (CD = FE), and solving the resulting equation:
10v = 16v - 12.

To determine the value of v that makes quadrilateral CDEF a parallelogram, we need to use the property that opposite sides of a parallelogram are equal in length.

Given:


\[ CD = 10v \]


\[ FE = 16v - 12 \]

For a parallelogram, opposite sides CD and FE must be equal:


\[ 10v = 16v - 12 \]

Now, solve for v:


\[ 10v - 16v = -12 \]

Combine like terms:


\[ -6v = -12 \]

Divide by -6 to isolate v:


\[ v = (-12)/(-6) = 2 \]

So, the value of
\(v\) that makes quadrilateral CDEF a parallelogram is
\(v = 2\). If
\(v = 2\), then CD and FE are equal in length, satisfying the condition for opposite sides of a parallelogram.

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