Question

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Answer 1

Answer:

Given - AB parallel to BC with a transversal EF

FP is the bisector of angle AEF and FQ is the bisector of angle EFD.

To Prove - EP is parallel to FQ

prove - if AB parallel to CD with transversal TF

Angle AEF = Angle BEF ( alternate interior angle)

So,

angle PEF= 1/2of angle AEF(EP bisect angle AEF)

angle EFQ =1/2 of angle BEF(FQ bisect angle angle BEF) ( angle AEF= BEF proved above so we can write AEF in the place of BEF)

from above..

angle PEF= EFQ

so line EP is parallel to FQ because angle PEF= EFQ is alternate interior angle and we know that is alternate interior angle are equal then the two line s are parallel.....

HoPe it help to you☺️❣️

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