Question

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

Answer 1

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.