Question

are these triangles similar?
s t (45), s u (35), u t (55); e d (54), e f (42), f d (66)
yes
no
write a similarity statement.
△ ~ △

Explanation:

Step1: Calculate the ratios of corresponding sides

For \(\triangle STU\) and \(\triangle EFD\), we check the ratios of their side lengths.
\(\frac{ST}{EF}=\frac{45}{42}=\frac{15}{14}\), \(\frac{TU}{FD}=\frac{55}{66}=\frac{5}{6}\), \(\frac{SU}{ED}=\frac{35}{54}\)

Wait, no, actually, we should match the sides properly. Let's check \(\frac{35}{42}=\frac{5}{6}\), \(\frac{45}{54}=\frac{5}{6}\), \(\frac{55}{66}=\frac{5}{6}\)

Step2: Determine similarity

Since \(\frac{SU}{EF}=\frac{35}{42}=\frac{5}{6}\), \(\frac{ST}{ED}=\frac{45}{54}=\frac{5}{6}\), \(\frac{TU}{FD}=\frac{55}{66}=\frac{5}{6}\)

By the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

For the similarity statement, we match the vertices based on the corresponding sides. \(SU\) corresponds to \(EF\), \(ST\) corresponds to \(ED\), \(TU\) corresponds to \(FD\)

So \(\triangle STU\sim\triangle EDF\)

Answer:

\(\triangle STU\sim\triangle EDF\)