Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your ans
which statement about the two triangles is correct?
you cannot tell if the triangles are similar because the angles are not given.
△abc is congruent to △def.
△abc is not similar to △def, because 12 - 8 = 4, while 9 - 6 = 3.
△abc ~ △def because \frac{6}{4}=\frac{12}{8}=\frac{9}{6}

Explanation:

Step1: Check congruence

For congruence, all corresponding sides must be equal. Here, \(12
eq8\), \(9
eq6\), \(6
eq4\). So \(\triangle ABC\) is not congruent to \(\triangle DEF\).

Step2: Check similarity ratio

Calculate the ratios of corresponding sides:

• \(\frac{AC}{DF}=\frac{6}{4}=\frac{3}{2}\)
• \(\frac{AB}{DE}=\frac{12}{8}=\frac{3}{2}\)
• \(\frac{BC}{EF}=\frac{9}{6}=\frac{3}{2}\)

Since \(\frac{AC}{DF}=\frac{AB}{DE}=\frac{BC}{EF}\), by the Side - Side - Side (SSS) similarity criterion, the triangles are similar.

Step3: Analyze other options

• For the first option, when the ratios of all three pairs of corresponding sides are equal (as we found), we can tell the triangles are similar without knowing the angles (by SSS similarity).
• For the third option, subtraction of side lengths is not a valid method to check similarity. Similarity is based on ratios of side lengths, not differences.

Answer:

\(\triangle ABC\sim\triangle DEF\) because \(\frac{6}{4}=\frac{12}{8}=\frac{9}{6}\) (the fourth option)