Question

1. which conclusion does the diagram support?

a $\frac{bc}{ab}=\frac{ed}{fe}$
b $\frac{ab}{bc}=\frac{ed}{fe}$
c $\frac{be}{cd}=\frac{af}{be}$
d $be = \frac{1}{2}cd$

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

When three or more parallel lines are cut by two transversals, the segments are proportional.
For the parallel lines and transversals in the given diagram, we have \(\frac{AB}{BC}=\frac{FE}{ED}\) (by the property of parallel - cut transversals).
Cross - multiplying gives \(\frac{AB}{BC}=\frac{FE}{ED}\Rightarrow\frac{AB}{BC}=\frac{ED}{FE}\) (by taking reciprocals).

Answer:

B. \(\frac{AB}{BC}=\frac{ED}{FE}\)