ABCD is a square. E,F,F and H are the mid points of AB,BC,CD and DA respectively. Such that AE=BF=CG=DH. Prove that EFGH is a square
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angle HAE = 90 °(ABCD is a square )
angle AEH = AHE = 45° (since all sides are equal and when divided through mp the all 8 parts became equal)
similar to all sides as in the diagram
hence
all sides are 90°
now ∆AHE,EBF,FCG,GDH
are same right angled ∆
therefore their hypotenuse(sides of square EFGH) is also same
therefore EFGH is a square
angle AEH = AHE = 45° (since all sides are equal and when divided through mp the all 8 parts became equal)
similar to all sides as in the diagram
hence
all sides are 90°
now ∆AHE,EBF,FCG,GDH
are same right angled ∆
therefore their hypotenuse(sides of square EFGH) is also same
therefore EFGH is a square
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