Question

f 12 10 u 30 36 t s \\( \triangle u t s \sim \\)____

Explanation:

Step1: Check the ratio of sides

We know that \(\frac{UT}{UE}=\frac{36}{10} = \frac{18}{5}\), \(\frac{US}{UF}=\frac{30}{12}=\frac{5}{2}\). Wait, no, actually, for similar triangles, if \(\angle FUE=\angle TUS\) (vertical angles are equal). And \(\frac{UF}{UT}=\frac{12}{36}=\frac{1}{3}\), \(\frac{UE}{US}=\frac{10}{30}=\frac{1}{3}\).

Step2: Use the Side - Angle - Side (SAS) similarity criterion

Since \(\frac{UF}{UT}=\frac{UE}{US}\) and \(\angle FUE=\angle TUS\) (vertical angles), by the SAS (Side - Angle - Side) similarity criterion, \(\triangle FUE\sim\triangle TUS\).

Answer:

\(\triangle FUE\)