Question

determine whether the triangles are similar. If similar, state how (AA, SSS, or SAS), and write a smiliarity statement.

Answer 1

Given two triangles :

The similar triangles have a corresponding congruent angles and the corresponding sides are in proportional

So, As shown :

The measure of angle F = the measure of angle T

So, the angles F and T are congruent

`\begin{gathered} (EF)/(GF)=(3)/(5) \\ \\ (RT)/(ST)=(9)/(15)=(3\cdot3)/(3\cdot5)=(3)/(5) \\ \\ So,(EF)/(GF)=(RT)/(ST)=(3)/(5) \end{gathered}`

So, the triangle EFG is similar to the triangle RTS

They are similar by SAS ( side - angle - side )

`\Delta EFG\approx\Delta RTS`