Question

if cd = v and cf = 3v - 64, find the value of v that makes quadrilateral defg a parallelogram. v =

Explanation:

Step1: Set equal diagonals segments

For DEFG to be a parallelogram, the diagonals bisect each other, so $CD = CF$.
$v = 3v - 64$

Step2: Rearrange to solve for $v$

Subtract $v$ from both sides, then add 64 to both sides.
$0 = 2v - 64$
$2v = 64$

Step3: Calculate final value of $v$

Divide both sides by 2.
$v = \frac{64}{2}$

Answer:

$v = 32$