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In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $AF = 8$ and $DF = 4$, then what is $BD$?

 Jul 9, 2021
 #1
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+1

                     A

                8

            F

         4

    D                            E

 

B                                       C

 

Because   EF  is parallel to  CD,  then  AF/ DF  =  AE  / EC

So     8 /4  =  AE  /EC =  2

So   AE =  2EC

 

And  because  DE  is parallel to  BC,  then    BD / DA  =  EC / AE

 

Then

BD / 12 =  EC / 2EC

BD / 12  =  1/2

BD  = 12 * (1/2)  =  6

 

cool cool cool

 Jul 9, 2021

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