Question

if gh = b and gj = 2b - 33, find gj in parallelogram hijk.

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, if the diagonals of parallelogram $HIJK$ are $HK$ and $IJ$ which intersect at $G$, then $GH = GJ$.

Step2: Set up the equation

Since $GH = b$ and $GJ=2b - 33$, and $GH = GJ$, we have the equation $b=2b - 33$.

Step3: Solve the equation for $b$

Subtract $b$ from both sides: $0 = 2b - b-33$, which simplifies to $b = 33$.

Step4: Find the value of $GJ$

Substitute $b = 33$ into the expression for $GJ$. So, $GJ=2\times33 - 33$.
$GJ=66 - 33=33$.

Answer:

$33$