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

Explanation

GIVEN A transversal PQ cuts two lines AB and CD at E and F respectively. EG and FH are the bisectors of a pair of corresponding angles `anglePEB` and `angleEFD` respectively such that `EG||FH`.
TO PROVE `ABB||CD`.
PROOF `EG||FH` are cut by the transversal EF.
`:. anglePEG=angleEFH" "("corres. "angles)`
`implies angleGEB=angleHFD`
`implies 2angleGEB=2angleHFD`
`implies anglePEB=angleEFD`
`[ :' angleGEB=1/2 anglePEB and angleHFD=1/2 angleEFD]`.
But, these are correcponding angles when AB and CD are cut by the transversal PQ.
`:. AB||CD` (by corres. `angles` axiom).