Question

lesson 9 practice problems

1. these two triangles are similar.

what are a and b? note: the two figures are not drawn to scale.

1. here is triangle abc. triangle xyz is similar to abc with scale factor 1/4.

Explanation:

Step1: Set up proportion for similar - triangles

For similar triangles, the ratios of corresponding sides are equal. For the first pair of similar triangles, we have the proportion $\frac{a}{10}=\frac{4}{b}=\frac{9}{15}$.

Step2: Solve for $a$

From $\frac{a}{10}=\frac{9}{15}$, cross - multiply: $15a = 9\times10$. Then $a=\frac{9\times10}{15}=6$.

Step3: Solve for $b$

From $\frac{4}{b}=\frac{9}{15}$, cross - multiply: $9b = 4\times15$. Then $b=\frac{4\times15}{9}=\frac{20}{3}$.

For the second problem, if triangle $XYZ$ is similar to triangle $ABC$ with a scale factor of $\frac{1}{4}$:
Let the sides of triangle $ABC$ be $AB = 4$, $BC = 5$, $AC = 7$. The sides of triangle $XYZ$ will be $XY=\frac{1}{4}\times AB=\frac{1}{4}\times4 = 1$, $YZ=\frac{1}{4}\times BC=\frac{1}{4}\times5=\frac{5}{4}$, $XZ=\frac{1}{4}\times AC=\frac{1}{4}\times7=\frac{7}{4}$.

Answer:

For the first problem: $a = 6$, $b=\frac{20}{3}$
For the second problem: The sides of triangle $XYZ$ are $XY = 1$, $YZ=\frac{5}{4}$, $XZ=\frac{7}{4}$