Question

3 determine javier draws triangles stu and xyz on the board. then he writes the quotients of the corresponding side lengths as fractions.
(\frac{xy}{st}=\frac{2}{8}) (\frac{yz}{tu}=\frac{3}{12}) (\frac{xz}{su}=\frac{4}{15})
javier says that (\triangle xyz) is not a dilation of (\triangle stu). is javier correct? how do you know?

Explanation:

Step1: Simplify the given ratios

Simplify $\frac{XY}{ST}=\frac{2}{8}=\frac{1}{4}$, $\frac{YZ}{TU}=\frac{3}{12}=\frac{1}{4}$, $\frac{XZ}{SU}=\frac{4}{15}$.

Step2: Check for dilation

In a dilation, the ratios of the corresponding - side lengths of two similar figures are equal. Here, $\frac{1}{4}
eq\frac{4}{15}$.

Answer:

Javier is correct. Since the ratios of the corresponding side - lengths $\frac{XY}{ST}$, $\frac{YZ}{TU}$, and $\frac{XZ}{SU}$ are not all equal, $\triangle XYZ$ is not a dilation of $\triangle STU$.