Question

12.
a. aa~
b. sss~
c. sas~
d. not similar

Explanation:

Step1: Calculate the ratios of corresponding sides

For the first triangle with sides \(8\), \(10\), \(15\) and the second triangle with sides \(12.8\), \(16\), \(24\).

• \(\frac{8}{12.8}=\frac{80}{128}=\frac{5}{8}\)
• \(\frac{10}{16}=\frac{10\div2}{16\div2}=\frac{5}{8}\)
• \(\frac{15}{24}=\frac{15\div3}{24\div3}=\frac{5}{8}\)

Step2: Check the similarity criterion

Since \(\frac{8}{12.8}=\frac{10}{16}=\frac{15}{24}\), by the SSS (Side - Side - Side) similarity criterion, if the ratios of the corresponding sides of two triangles are equal, then the two triangles are similar.

Answer:

B. \(SSS\sim\)