Which conclusion does the diagram support?

Answer:

The conclusion supported by the diagram is;

(A)  [tex]\dfrac{AB}{BC} = \dfrac{FE}{ED}[/tex]

Step-by-step explanation:

The question is examines the theorem that two transversals cut by three or more parallel lines are proportionally divided by the transversals

The given parallel lines are;

Line CD, line BE, and line line AB

The given transversals are;

Line AC and line DF

Therefore, by the above three or more parallel lines cutting two transversal theorem, we have;

BC/AB = ED/FE, BC/DF = AB/FE, CA/AB = DF/FE

From BC/AB = ED/FE, we find the inverse of both sides to get;

[tex]\dfrac{1}{\dfrac{BC}{AB} } = \dfrac{1}{\dfrac{ED}{FE} }[/tex]

[tex]\dfrac{1}{\dfrac{BC}{AB} } = \dfrac{AB}{BC} \ and \ \dfrac{1}{\dfrac{ED}{FE} } = \dfrac{FE}{ED}[/tex]

[tex]\therefore \ \dfrac{AB}{BC} = \dfrac{FE}{ED}[/tex]

The correct option is [tex]\dfrac{AB}{BC} = \dfrac{FE}{ED}[/tex]

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