Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
which statement about ( \triangle abc ) and ( \triangle def ) is true?
they are congruent
they are not similar because corresponding sides are not proportional.
they are not similar because ( overline{fd} ) is 8 more than ( overline{ca} ), while ( overline{de} ) is 5 more than ( overline{ab} ).
they are similar because ( overline{de} ) is twice as long as ( overline{ab} ), and ( overline{ef} ) is twice as long as ( overline{bc} ).

Explanation:

Step1: Calculate the ratios of corresponding sides

For \(\triangle ABC\) and \(\triangle DEF\), assume the correspondence \(AB\) with \(DE\), \(BC\) with \(EF\), \(CA\) with \(FD\).
\(AB = 5\), \(DE=10\), ratio \(\frac{DE}{AB}=\frac{10}{5} = 2\)
\(BC = 8\), \(EF = 16\), ratio \(\frac{EF}{BC}=\frac{16}{8}=2\)
\(CA=6\), \(FD = 12\) (assuming correct correspondence, if we check the ratios for similarity criteria)

Step2: Check similarity criteria

By the Side - Side - Side (SSS) similarity criterion, if \(\frac{DE}{AB}=\frac{EF}{BC}=\frac{FD}{CA}\), the triangles are similar.
Since \(\frac{DE}{AB}=\frac{EF}{BC} = 2\) (and if \(FD = 12\), \(\frac{FD}{CA}=\frac{12}{6}=2\))

Answer:

They are similar because \(\overline{DE}\) is twice as long as \(\overline{AB}\), and \(\overline{EF}\) is twice as long as \(\overline{BC}\)