Question

If the bisectors of a pair of alternate angles formed by a transversal with two given lines are parallel, prove that the given lines are parallel.

PLEASE HELP!​

Answer 1

$\huge\mathfrak{Bonjour!!}$

$\huge\bold\purple{Answer:-}$

⏩In order to prove that AB || CD, it is sufficient to show that,

angle AGH = angle DHG

Now, GM is the bisector of angle AGH and HL is the bisector of angle DHG

=> angle 1 = angle 2 and angle 3 = angle 4 [ consider it as equation (1)]

It is given that GM || HL and transversal EF interests them at G and H respectively.

Therefore,

angle 2 = angle 3 [Alternate angles]

=> angle 1 = angle 4 [ Therefore, angle 2 = angle 1 and angle 3 = angle 4, from (1)]

Therefore,

angle 1 + angle 2 = angle 3 + angle 4

=> angle AGH = angle DHG

=> AB || CD [Hence proved]

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Hope it helps...:-)

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