Question

problem 7: spiral review
triangle efg is similar to triangle efg.
determine the missing values and explain your thinking.

Explanation:

Step1: Find the scale factor

Since the triangles are similar, the ratio of corresponding sides is the same. The ratio of \(E'F'\) to \(EF\) (assuming \(EF = 10\) and \(E'F'=4\)) gives the scale factor. Let the scale factor \(k=\frac{4}{10}=\frac{2}{5}\)

Step2: Find the length of \(E'G'\)

We know that \(\frac{E'G'}{EG}=\frac{2}{5}\). If \(EG = 15\), then \(E'G'=\frac{2}{5}\times15 = 6\)

Step3: Find the length of \(FG\)

We know that \(\frac{F'G'}{FG}=\frac{2}{5}\). If \(F'G' = 9\), then \(FG=\frac{9}{\frac{2}{5}}=\frac{9\times5}{2}=22.5\)

Answer:

The length of \(E'G'\) is \(6\) and the length of \(FG\) is \(22.5\)