Question

29 how are these triangles similar? a aa b sss c not similar d sas

Explanation:

Step1: Calculate the ratios of corresponding sides

For \(\triangle BCD\) and \(\triangle FGH\):

• \(\frac{BD}{FG}=\frac{13.5}{30}=\frac{9}{20}\)
• \(\frac{CD}{GH}=\frac{18}{22.5}=\frac{4}{5}\)
• \(\frac{BC}{FH}=\frac{27}{45}=\frac{3}{5}\)

Since \(\frac{BD}{FG}
eq\frac{CD}{GH}
eq\frac{BC}{FH}\), we check another way.

Let's assume the correspondence \(B - F\), \(C - H\), \(D - G\)
\(\frac{BD}{FG}=\frac{13.5}{30}=\frac{9}{20}\) (wrong)

Let's assume the correspondence \(B - G\), \(C - H\), \(D - F\)
\(\frac{BD}{GF}=\frac{13.5}{30}=\frac{9}{20}\) (wrong)

Let's assume the correspondence \(B - F\), \(C - G\), \(D - H\)
\(\frac{BD}{FH}=\frac{13.5}{45}=\frac{3}{10}\) (wrong)

Let's assume the correspondence \(B - G\), \(C - F\), \(D - H\)
\(\frac{BD}{GH}=\frac{13.5}{22.5}=\frac{3}{5}\)
\(\frac{CD}{FH}=\frac{18}{45}=\frac{2}{5}\) (wrong)

Let's assume the correspondence \(B - H\), \(C - G\), \(D - F\)
\(\frac{BD}{HF}=\frac{13.5}{45}=\frac{3}{10}\) (wrong)

Let's assume the correspondence \(B - H\), \(C - F\), \(D - G\)
\(\frac{BD}{HG}=\frac{13.5}{22.5}=\frac{3}{5}\)
\(\frac{CD}{FG}=\frac{18}{30}=\frac{3}{5}\)
\(\frac{BC}{FH}=\frac{27}{45}=\frac{3}{5}\)

Since \(\frac{BD}{HG}=\frac{CD}{FG}=\frac{BC}{FH}=\frac{3}{5}\)

Answer:

B. SSS