Question

geometry - 103
6 - 3: lesson quiz
due sep 23 - 11:45 pm late
if wy + xz = 28, what is pz?
pz = choose...

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, the diagonals bisect each other. So $WY = 2WP$ and $XZ=2PZ$, and $WY + XZ=2(WP + PZ)$. Also, $WP + PZ = WZ$ and the diagonals of parallelogram $WXYZ$ bisect each other, so $WY=2WP$ and $XZ = 2PZ$. Given $WY+XZ = 28$, we know that $2(WP + PZ)=28$, and since $WP=8$.

Step2: Substitute and solve

Let $PZ=x$. We know that $WY + XZ=2(WP + PZ)$. Substitute $WY + XZ = 28$ and $WP = 8$ into the equation: $28=2(8 + x)$. First, divide both sides of the equation by 2: $\frac{28}{2}=8 + x$, which simplifies to $14=8 + x$. Then subtract 8 from both sides: $x=14 - 8$.

Answer:

$6$