Question

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

Answer 1

Given : Two lines AB and CD are interesected by a transversal EF and GH are bisectors of `anglePEB and angle EGD` respectively
Also EF||GH
To Prove: AB||CD
Proof : When EF||GH and l cuts them,

`:. angle1= angle3` (corresponding angles)
`rArr 2 angle1=2angle3`
`rArr angle 1+angle2=angle3+angle4`
`( :. angle1= angle2 and angle3 =4 ` as EF and GH are anlge bisectors )

But these are the corresponding angles for 3 necessary lines AB, CD and l
`:. AB||CD `