Question

if two lines are parallel then prove that any pair of bisected of their alternate interior angle is also parallel.
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Answer 1

Step-by-step explanation:

refer to the above attachment

Answer 2

Answer:

GIVEN AB∣∣CD are cut by a transversal t at E and F respectively, EG and FH are the bisectors of a pair of alt. int. ∠s,∠AEF and anl≥EFD respectively.

TO PROVE EG∣∣FH,

PROOF Since AB∣∣CD and t is a transversal, we have :

∠AEF=∠EFD [alt. int. ∠s]

⇒12∠AEF=12∠EFD

⇒∠GEF=∠EFH.

But, these are alternate interior angles formed when the transversal EF cuts EG and FH.

∴EG∣∣FH.

Hope it helps you !