Question

if de = 2s + 10 and dg = 4s + 2, find the value of s that makes quadrilateral efgh a parallelogram.

Explanation:

Step1: Set segments equal (parallelogram diagonals bisect)

$DE = DG$

Step2: Substitute given expressions

$2s + 10 = 4s + 2$

Step3: Rearrange to solve for $s$

$10 - 2 = 4s - 2s$
$8 = 2s$
$\frac{8}{2} = s$

Answer:

$s = 4$