Question

if $ce = 8z$ and $cg = 4z + 8$, find the value of $z$ that makes quadrilateral $defg$ a parallelogram.

Explanation:

Step1: Set segments equal (diag. bisect)

For DEFG to be a parallelogram, its diagonals bisect each other, so $CE = CG$.

Step2: Substitute given expressions

$8z = 4z + 8$

Step3: Isolate z term

Subtract $4z$ from both sides:
$8z - 4z = 8$
$4z = 8$

Step4: Solve for z

Divide both sides by 4:
$z = \frac{8}{4}$

Answer:

$z = 2$