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Given that the corresponding lengths are equal, find AB : BC.

 

 Jan 22, 2021
 #1
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+1

AB : BC = 3 : 1

 Jan 22, 2021
 #2
avatar+116126 
+1

Let G  be located on AC  such that  FG is   parallel to   CD

 

angle GFB  = angle CEB

BF  = BE

And angle CBE  = angle  FBG

 

So by ASA  triangle FBG  is congruent  to triangle EBC

 

So  BG  = BC

 

But since    AF   =  AD   then   GA  also =  GC

 

But  BC  +  BG   =    GC

 

And since BG  = BC  then      2BC  =  GC

 

So 2BC also   =  GA

 

And  AC =  GC + GA     =    2BC  + 2BC   =  4BC

 

And AB =   4BC  - BC   = 3BC

 

So

 

AB : BC    =   3 : 1            { just as the  guest found !!! }

 

 

cool cool cool

 Jan 22, 2021

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