Question

ABCD is a square. E,F,G 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.

Answer 1

here is ur answer..
hope it helps u..

Answer 2

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.

${\fcolorbox{blue}{black}{\underline{\blue{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:HumanIntelligence\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}}$