Answer:
Segment BF = 16
Step-by-step explanation:
The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately
The given theorem is the Triangle Proportionality Theorem
According to the theorem, given that segment DE is parallel to segment BC, we have;
[tex]\dfrac{AD}{BD} = \dfrac{AE}{EC}[/tex]
Therefore;
[tex]BD = \dfrac{AD}{\left(\dfrac{AE}{EC} \right) } = AD \times \dfrac{EC}{AE}[/tex]
Which gives;
[tex]BD = 6 \times \dfrac{18}{12}= 9[/tex]
Similarly, given that EF is parallel to AB, we get;
[tex]\dfrac{AE}{EC} = \dfrac{BF}{FC}[/tex]
Therefore;
[tex]BF = FC \times \dfrac{AE}{EC}[/tex]
Which gives;
[tex]BF = 24 \times \dfrac{12}{18} = 16[/tex]
Therefore, the statement that can be proved using the given theorem is segment BF = 16.
