Question

determine if the given triangles are similar if they are select the option that includes a similarity statement with the justifying prostulaye or theorem them they are not select option states such

Answer 1

We are asked to determine if the given triangles are similar or not.

Let us find the rato of the corresponding sides

$\begin{gathered} \frac{GA}{BE}=\frac{GU}{EF} \\ \frac{12}{15}=\frac{16}{20} \\ \frac{4}{5}=\frac{4}{5} \end{gathered}$

So, △GUA and △EFB have two equal sides since the ratio of the two corresponding sides is equal.

$\begin{gathered} GA\sim BE \\ GU\sim EF \end{gathered}$

Also, notice that the one corresponding angle is equal

$\angle G\cong\angle E$

Hence, the triangles △GUA and △EFB are similar by SAS theorem since the ratio of two corresponding sides is equal and one included angle is also equal.

Therefore, the last option is the correct answer.