Answer:
Option (3)
Step-by-step explanation:
"If two triangles are similar, their corresponding sides are proportional."
We will check each proportionality ratio given in the options for the given property,
Option (1),
[tex]\frac{QB}{DM}=\frac{DF}{QL}=\frac{LB}{MF}[/tex]
[tex]\frac{3.5}{2}=\frac{5}{8.75}=\frac{10.5}{6}[/tex]
[tex]\frac{7}{4}=\frac{4}{7}=\frac{7}{4}[/tex]
But [tex]\frac{7}{4}\neq \frac{4}{7}[/tex].
Therefore, this option is not the answer.
Option (2),
[tex]\frac{FM}{LB}=\frac{BQ}{MD}=\frac{QL}{DF}[/tex]
[tex]\frac{6}{10.5}=\frac{3.5}{2}=\frac{8.75}{5}[/tex]
[tex]\frac{4}{7}=\frac{7}{4}=\frac{7}{4}[/tex]
But [tex]\frac{4}{7}\neq \frac{7}{4}[/tex],
Therefore, this option is not the option.
Option (3),
[tex]\frac{BQ}{MD}=\frac{QL}{DF}=\frac{BL}{MF}[/tex]
[tex]\frac{3.5}{2}=\frac{8.75}{5}=\frac{10.5}{6}[/tex]
[tex]\frac{7}{4}=\frac{7}{4}=\frac{7}{4}[/tex]
Therefore, this option is the answer.
Option (4),
[tex]\frac{6}{10.5}=\frac{2}{3.5}=\frac{5}{10.5}[/tex]
[tex]\frac{4}{7}=\frac{4}{7}=\frac{10}{21}[/tex]
But, [tex]\frac{4}{7}\neq \frac{10}{21}[/tex]
Therefore, this is not the correct option.
