Question

plz answer this question​

Answer 1

R.E.F image

Given : ABCD is A parallelogram

To Prove : BF=BC

Proof : In △DCE,DE=DC (given)

∴∠DCE=∠DEC...(1)

(Equal sides have equal is opposite to them)

since,

AB∥CD,∠DCE=∠BFC...(2) (pair of corresponding ∠S)

Form (1) and (2)

∠DEC=∠BFC

In △AEF,∠AEF=∠AFE

∴AF=AE,

⇒AB+BF=AD+DE

⇒BF=AD [∵AB=CD=DE]

⇒BF=BC [∵AD=BC] Hence proved

Answer 2

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Given :

ABCD is A parallelogram

To Prove :

BF=BC

Proof :

In △DCE,DE=DC (given)

∴∠DCE=∠DEC...(1)

(Equal sides have equal is opposite to them)

since,

AB∥CD,∠DCE=∠BFC...(2) (pair of corresponding ∠S)

Form (1) and (2)

∠DEC=∠BFC

In △AEF,∠AEF=∠AFE

∴AF=AE,

⇒AB+BF=AD+DE

⇒BF=AD [∵AB=CD=DE]

⇒BF=BC [∵AD=BC] Hence proved.