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} (GA)/(BE)=(GU)/(EF) \\ (12)/(15)=(16)/(20) \\ (4)/(5)=(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.