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

Learn More:

In the adjoining figure two parallelogram ABCD and AEFB are ...

https://brainly.in/question/13596062

in fig.1 ,AM and CN are perpendicular to the diagonal BD of a ...

https://brainly.in/question/7373513