Similar triangles may or may not be congruent.
The value of EF is 15.
[tex]\mathbf{ABC \sim \triangle DE F}[/tex] means that:
[tex]\mathbf{AB \sim D E}[/tex]
[tex]\mathbf{BC \sim EF}[/tex]
[tex]\mathbf{AC \sim DF}[/tex]
So, the equivalent ratio is:
[tex]\mathbf{EF:BC = DF:AC}[/tex]
Where:
[tex]\mathbf{BC = 18, DF = 10, AC = 12}[/tex]
Substitute these values in [tex]\mathbf{EF:BC = DF:AC}[/tex]
[tex]\mathbf{EF:18 = 10:12}[/tex]
Express as fractions
[tex]\mathbf{\frac{EF}{18} = \frac{10}{12}}[/tex]
Multiply both sides by 18
[tex]\mathbf{EF = \frac{10}{12} \times 18}[/tex]
Simplify
[tex]\mathbf{EF = \frac{10}{2} \times 3}[/tex]
[tex]\mathbf{EF = 5 \times 3}[/tex]
[tex]\mathbf{EF = 15}[/tex]
Hence, the value of EF is 15.
Read more about similar triangles at:
https://brainly.com/question/14926756
