SOLUTION: Hello! I've been asked by my teacher to solve the following proof: Prove: If two parallel lines are cut by a transversal, then bisectors of corresponding angles are parallel.

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Question 31170: Hello! I've been asked by my teacher to solve the following proof:
Prove: If two parallel lines are cut by a transversal, then bisectors of corresponding angles are parallel.

I have tried this problem over and over but I cant seem to picture it. Therefore I'm having problems solving it. Please help! Thank You.
Found 3 solutions by venugopalramana, cleomenius, Sanjana01:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
LET AB AND CD BE THE PARALLEL LINES.LET XY BE A TRANSVERSAL CUTTING AB AT P AND CD AT Q.LET EF BE THE BISECTOR OF ANGLE XPB AND GH THE BISECTOR OF ITS CORRESPONDING ANGLE XQD.
CORRESPONDING ANGLES ARE EQUAL SO..
ANGLE XPB=ANGLE XQD....SINCE EF AND GH ARE THEIR BISECTORS....WE HAVE ....
ANGLE XPF = ANGLE XPB/2 = ANGLE XQD/2 = ANGLE XQH....SO.....
WE HAVE 2 LINES EF AND GH ,A TRANSVERSAL XPQY CUTS THEM AT P AND Q RESPECTIVELY.
AND....ANGLE XPF = ANGLE XQH...WHICH ARE CORRESPONDING ANGLES . HENCE EF IS PARALLEL TO GH.SO THE BISECTORS OF CORRESPONDING ANGLES ARE PARALLEL.

Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
Let lines AB and CD be parallel lines.
Let transversal EF cross AB and CD.
Let angle 1 and angle 2 be corresponding angles formed by EF crossing lines AB and CD.
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Statement: Angle 1 is congruent to angle 2.
Reason: Theorem, if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
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Statement: 1/2 angle 1 = 1/2 angle 2 (They are congruent).
Reason: Definition of Bisector.
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Statement: The bisectors of angles 1 and angle 2 are parallel.
Reason. Theorem, if 2 lines cut be a tranversal form a pair of corresponding angles with the transversal, then the lines are parallel.
Cleomenius.

Answer by Sanjana01(2) About Me  (Show Source):
You can put this solution on YOUR website!
this is what my teacher did -
visit link
https://docs.google.com/drawings/d/1moRQ8lVM61WxX0HoP9x_p5nF-9L2-6wnC3ctyOJTM3k/edit?usp=sharing