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avatar+464 

here is the question

 

 Oct 11, 2018

Best Answer 

 #1
avatar+7350 
+1

∠AEB  ≅  ∠CED   because they are vertical angles

∠EAB  ≅  ∠ECD   because they are alternate interior angles

So by the AA similarity theorem, △EAB ~ △ECD

 

Since △EAB ~ △ECD,

CD / AB  =  DE / BE

100 / 150  =  DE / BE

2 / 3  =  DE / BE

 

∠BCD  ≅  ∠BFE   because they are corresponding angles

∠BDC  ≅  ∠BEF   because they are corresponding angles

So by the AA similarity theorem, △BCD ~ △BFE

 

Since △BCD ~ △BFE,

DC / EF  =  BD / BE                       And    DC  = 100     and     BD  =  BE + DE

100 / EF  =  (BE + DE) / BE           Distribute  1 / BE  to the terms in parenthesees.

100 / EF  =  BE / BE + DE / BE

100 / EF  =  1 + DE / BE                And  DE / BE  =  2 / 3

100 / EF  =  1 + 2 / 3

100 / EF  =  5 / 3                Multiply both sides of the equation by  3 .

300 / EF  =  5                     Multiply both sides of the equation by  EF .

300  =  5 * EF                    Divide both sides of the equation by  5 .

60  =  EF

 

The number of centimeters in the length of EF is  60 .

 Oct 11, 2018
 #1
avatar+7350 
+1
Best Answer

∠AEB  ≅  ∠CED   because they are vertical angles

∠EAB  ≅  ∠ECD   because they are alternate interior angles

So by the AA similarity theorem, △EAB ~ △ECD

 

Since △EAB ~ △ECD,

CD / AB  =  DE / BE

100 / 150  =  DE / BE

2 / 3  =  DE / BE

 

∠BCD  ≅  ∠BFE   because they are corresponding angles

∠BDC  ≅  ∠BEF   because they are corresponding angles

So by the AA similarity theorem, △BCD ~ △BFE

 

Since △BCD ~ △BFE,

DC / EF  =  BD / BE                       And    DC  = 100     and     BD  =  BE + DE

100 / EF  =  (BE + DE) / BE           Distribute  1 / BE  to the terms in parenthesees.

100 / EF  =  BE / BE + DE / BE

100 / EF  =  1 + DE / BE                And  DE / BE  =  2 / 3

100 / EF  =  1 + 2 / 3

100 / EF  =  5 / 3                Multiply both sides of the equation by  3 .

300 / EF  =  5                     Multiply both sides of the equation by  EF .

300  =  5 * EF                    Divide both sides of the equation by  5 .

60  =  EF

 

The number of centimeters in the length of EF is  60 .

hectictar Oct 11, 2018
 #2
avatar+98107 
+1

Nice, hectictar  !!!

 

 

cool cool cool

CPhill  Oct 11, 2018
 #3
avatar+464 
+1

Thank you hectictar

 Oct 11, 2018

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