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

$\begin{gathered} \frac{EF}{GF}=\frac{3}{5} \\ \\ \frac{RT}{ST}=\frac{9}{15}=\frac{3\cdot3}{3\cdot5}=\frac{3}{5} \\ \\ So,\frac{EF}{GF}=\frac{RT}{ST}=\frac{3}{5} \end{gathered}$

So, the triangle EFG is similar to the triangle RTS

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

$\Delta EFG\approx\Delta RTS$