Answer:
Option C
Step-by-step explanation:
Two triangles are similar if they have at least 2 equal angles
Note that the HEF triangle has angles of 90 °, 60 ° and 30 °
Note that the EGF triangle has angles of 90 ° and 30 ° so the third angle must be 60 °
Then HEF and EGF are similar triangles.
By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' c' then
[tex]\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}=k[/tex]
Where the constant k is known as "scale factor"
In this case
[tex]\frac{HF}{EF}=\frac{HE}{EG}=\frac{FE}{GF}=k[/tex]
[tex]k=\frac{3}{\sqrt{3}}=\frac{2\sqrt{3}}{2}=\frac{\sqrt{3}}{1}=\sqrt{3}[/tex]
[tex]\frac{FE}{GF}=\frac{\sqrt{3}}{1}[/tex]
or
[tex]\sqrt{3}:1[/tex]
The answer is Option C
