Question

what proportional - segment lengths verify that $overline{xz}paralleloverline{pq}$? fill in the boxes to correctly complete the proportion. $\frac{16}{21}=\frac{square}{square}$

Explanation:

Step1: Recall similarity - side - ratio property

If $\overline{XZ}\parallel\overline{PQ}$, then $\frac{XP}{PY}=\frac{ZQ}{QY}$. Given $XP = 5$, $PY=16$, $ZQ = 2.5$, and $QY = 8$. We can also use the property of similar - triangles formed by parallel lines. The ratio of corresponding sides of similar triangles is equal.
We know that $\frac{XP}{XP + PY}=\frac{ZQ}{ZQ+QY}$. Let's find the ratio of the segments of one side and apply it to the other side.
We have $\frac{XP}{PY}=\frac{5}{16}$ and $\frac{ZQ}{QY}=\frac{2.5}{8}=\frac{25}{80}=\frac{5}{16}$.
The proportion for the whole - side segments: $\frac{XP}{XY}=\frac{ZQ}{ZY}$. Here, $XY=XP + PY=5 + 16=21$ and $ZY=ZQ + QY=2.5+8 = 10.5$.
The proportion is $\frac{5}{21}=\frac{2.5}{10.5}$.

Step2: Fill in the proportion

The proportion is $\frac{5}{21}=\frac{2.5}{10.5}$.

Answer:

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