let AB and CD be parallel lines with EF a transversal cutting AB at P and CD at Q
by properties of parallel lines (PPL)
<EPB = <PQD = a
<BPQ = <DQF = b
let PO be the bisector of <EPB and
let QR be the bisector of <PQD
then <OPB = a/2 and
<RQD = a/2
<FQR = b + a/2
<QPO = b + a/2
therefore <FQR = <QPO (but they are corresponding angles)
so PO || QR
How would I prove the following (With a formal mathematical proof)?:
If a transversal intersects two parallel lines, then the bisectors of two corresponding angles are parallel.
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