Question

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.​

Answer 1

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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