Question

eleonore wants to prove that if a line divides two sides in a triangle proportionally, then it is parallel to the third side.

image of triangle abc with points e on ac and d on ab, and segment ed

select the appropriate rephrased statement for eleonores proof.

choose 1 answer:

a in △abc, if $overleftrightarrow{ed} \parallel \overline{cb}$, then $dfrac{ae}{ec} = dfrac{ad}{db}$.

b in △abc, if $dfrac{ae}{ec} = dfrac{ad}{db}$, then $overleftrightarrow{ed} \parallel \overline{cb}$.

c in △abc, if $overleftrightarrow{ed} \parallel \overline{cb}$, then $dfrac{ae}{ec} = dfrac{ed}{cb}$.

d in △abc, if $dfrac{ae}{ec} = dfrac{ed}{cb}$, then $overleftrightarrow{ed} \parallel \overline{cb}$.

Explanation:

The original statement is: if a line divides two sides of a triangle proportionally, then it is parallel to the third side. For $\triangle ABC$, line $\overleftrightarrow{ED}$ divides sides $AC$ and $AB$ into segments $\frac{AE}{EC} = \frac{AD}{DB}$ (proportional division), so the conclusion is $\overleftrightarrow{ED} \parallel \overline{CB}$. This matches option B.

Answer:

B. In $\triangle ABC$, if $\frac{AE}{EC} = \frac{AD}{DB}$, then $\overleftrightarrow{ED} \parallel \overline{CB}$.