Question

question 9 of 12 (1 point) | question attempt: 1 of unlimited
△abc and △xyz are similar.
(a) complete the three pairs of proportions below.
ratio of lengths of sides of △abc
\\(\frac{ab}{ac}=\square\\) \\(\frac{ab}{bc}=\square\\) \\(\frac{ac}{bc}=\frac{4}{5})
ratio of the lengths of sides of △xyz that correspond to the sides of △abc in the ratio above
\\(\frac{?}{xz}=\frac{1}{2}) \\(\frac{?}{yz}=\frac{2}{5}) \\(\frac{xz}{?}=\square\\)

Explanation:

Step1: Calculate $\frac{AB}{AC}$

Given $AB = 6$ and $AC=12$, so $\frac{AB}{AC}=\frac{6}{12}=\frac{1}{2}$

Step2: Calculate $\frac{AB}{BC}$

Given $AB = 6$ and $BC = 15$, so $\frac{AB}{BC}=\frac{6}{15}=\frac{2}{5}$

Step3: Find the missing - ratio for $\frac{XZ}{YZ}$

Since $\frac{AC}{BC}=\frac{12}{15}=\frac{4}{5}$, and the triangles are similar, the corresponding - ratio for $\triangle XYZ$ is $\frac{XZ}{YZ}$. Given $XZ = 20$ and $YZ = 25$, $\frac{XZ}{YZ}=\frac{20}{25}=\frac{4}{5}$

Answer:

$\frac{AB}{AC}=\frac{1}{2}$, $\frac{AB}{BC}=\frac{2}{5}$, $\frac{XZ}{YZ}=\frac{4}{5}$