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Question -

ABCD is a square E, F, G and H are points on AB, BC, CD and DA respectively. such that AE = BF = CG = DH. Prove that EFGH is a square.



Answer -

Square ABCD is given:
 
E, F, G and H are the points on AB, BC, CD and DA respectively, such that :
 
We need to prove that EFGH is a square.
Say,  
As sides of a square are equal. Then, we can also say that:
 
In  and  ,we have:
  (Given)
  (Each equal to 90°)
  (Each equal to y )
By SAS Congruence criteria, we have:
 
Therefore, EH = EF
Similarly, EF= FG, FG= HG and HG= HE
Thus, HE=EF=FG=HG
Also,
  and  
But,
  and  
Therefore,
 
i.e.,  
Similarly,
 
 
 
Thus, EFGH is a square.
Hence proved.


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