Question -
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.