Question

what proportional segment lengths verify that xz ∥ pq? fill in the boxes to correctly complete the proportion.
\frac{16}{}=\frac{}{}

Explanation:

Step1: Apply similar - triangle property

Since $\overline{XZ}\parallel\overline{PQ}$, we have $\triangle XPQ\sim\triangle XYZ$. Then the ratios of corresponding sides are equal. That is $\frac{XP}{XY}=\frac{XQ}{XZ}$. Given $XP = 5$, $XY=5 + 16=21$, and $XQ = 2.5$. Let $XZ=x$. So $\frac{5}{21}=\frac{2.5}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{5}{21}=\frac{2.5}{x}$ gives us $5x=2.5\times21$.

Step3: Solve for $x$

$5x = 52.5$, then $x=\frac{52.5}{5}=10.5$. The proportion to complete is $\frac{5}{21}=\frac{2.5}{10.5}$.

Answer:

$\frac{5}{21}=\frac{2.5}{10.5}$