Question

If in triangle ABC and DEF, AB/DE=BC/FD then they will be similar when and here are the options A) <B=<E and B) <A=<D and C)<B=<D and D)<A=<F . FIND THE ANSWER THEN!?

Answer 1

C) Given in ∆ABC and ∆EDF,

By converse of basic proportional theory,
∆ABC ~ ∆ EDF
Angle B = Angle D
Angle A = Angle E
Angle C = Angle F

Hope this helps you friend
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Answer 2

Given : ΔABC and ΔDEF

AB/DE  = BC/FD  

To Find : Condition for triangles to be similar

A) ∠B=∠E and B) ∠A=∠D and C)∠B=∠D and D)∠A=∠F

Solution:

Triangle are similar is ratio of corresponding sides is equal  by SSS similarity

so if   AC/EF  =  AB/DE  = BC/FD  

Then ΔABC ~ ΔEDF

or using  SAS   similarity   if  

Ratio of two corresponding sides is equal and included angles are Equal then triangles are similar

so    AB/DE  = BC/FD  

and ∠B = ∠D

Then ΔABC ~ ΔEDF   using SAS  similarity

Hence Either   AC/EF  =  AB/DE  = BC/FD      or  ∠B = ∠D

Then triangles are similar

from the given options correct option is option  C)∠B=∠D

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