Question

decide whether the triangles are similar. if they are, write a similarity statement and state the reason justifying the simila if necessary, you may learn what the markings on a figure indicate.

(figure with triangle abc: ab=8, bc=10, ac=16; triangle def: de=4, ef=8, fd=5)

options:

• not similar or not necessarily similar
• similar:

△abc ~ △ by the

Explanation:

Step1: Identify side lengths

For $\triangle ABC$: $AB = 8$, $BC = 10$, $AC = 16$. For $\triangle DEF$ (assuming labels): $DE = 4$, $DF = 5$, $EF = 8$.

Step2: Check ratios

$\frac{AB}{DE}=\frac{8}{4}=2$, $\frac{BC}{DF}=\frac{10}{5}=2$, $\frac{AC}{EF}=\frac{16}{8}=2$. Ratios are equal.

Step3: Determine similarity

By SSS (Side - Side - Side) similarity criterion, if corresponding sides are proportional, triangles are similar. So $\triangle ABC \sim \triangle DEF$ (order based on side ratios: $AB$ corresponds to $DE$, $BC$ to $DF$, $AC$ to $EF$).

Answer:

Similar: $\triangle ABC \sim \triangle DEF$ by the SSS (Side - Side - Side) Similarity Criterion