Question

Which conclusion does the diagram support?

Answer 1

The conclusion supported by the diagram is;

(A)
`(AB)/(BC) = (FE)/(ED)`

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;

`(1)/((BC)/(AB) ) = (1)/((ED)/(FE) )`

`(1)/((BC)/(AB) ) = (AB)/(BC) \ and \ (1)/((ED)/(FE) ) = (FE)/(ED)`

`\therefore \ (AB)/(BC) = (FE)/(ED)`

The correct option is
`(AB)/(BC) = (FE)/(ED)`