ABCD is a square. E, F, G and H are points on AB, BC, CD, and DA respectively, such that AE = BF = CD = DH. Prove that EFGH is a square.
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Given AE=BF=CG=DH
⟹ So, EB=FC=GD=HA
In △s AEH and BFE,
AE=BF, AH=EB,
∠A=∠B (each ∠ = 90⁰)
∴ △AEH ≅ △BFE
⟹ EH=EF and ∠4= ∠2.
But ∠1 + ∠4 = 90⁰ ⟹ ∠1 + ∠2 = 90⁰
⟹ ∠HEF = 90⁰
And if ∠HEF = 90⁰ so, ∠EFG = 90⁰, ∠FGH = 90⁰ and ∠GHE = 90⁰.
Hence Proved.
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