Question

In the figure,ABCD is a parallelogram and AE=BF=CG=DH.Prove that EFGH is a parallelogram​

Answer 1

Given : ABCD is a parallelogram and AE=BF=CG=DH

To Find : .Prove that EFGH is a parallelogram​

Solution:

AE=BF=CG=DH.

ABCD is a parallelogram

opposites sides are equal

Opposite angles are equal

=> AB = CD   and BC = AD  

∠A = ∠C

∠B = ∠D

AB = CD

AE =CG

AB - AE = CD - CG

BE = DG

in ΔHDG  and Δ FBE

DH. = BF  given

∠D = ∠B

DG = E  ( shown above)

=> ΔHDG ≅  Δ FBE

=> HG = FE

Similarly we can show that

ΔGCF ≅  Δ EAH

=> GF = EH

HG = FE

GF = EH

Pair of opposites sides are equal

Hence EFGH is a parallelogram​

QED

Hence proved

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