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$ABCD$ is a parallelogram. The point $E$ is in the segment $BC$, and $F$ is a point in the line $DC$ such that $AF$ pass through the point $E$ and intersect the segment $BD$ in the point $G$. If $AG=6$ and $GE=4$. How long is $EF$?

 

 Jan 28, 2021
 #1
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Triangle  DGA ≈    Triangle  BGE

GE/ GA =  EB /AD

4/6  =  EB / AD

2/3  = EB /AD              {   AD   =  BC  }

2/3  = EB / BC

(2/3)BC = EB

So  EC  =(1/3) BC

So  EB/ EC   = 2/1

So  EC /EB  =  1/2

 

And

Triangle   AEB  ≈  FEC

EF / AE =   EC /EB

EF /10  =  1/2

EF   = 5

 

 

cool cool cool

 Jan 28, 2021

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