Question -
Answer -
Given AB and CD are straight lines which intersect at O.
OP is the bisector of┬атИа AOC.
To Prove : OQ is the bisector of┬атИаBOD
Proof :
AB, CD and PQ are straight lines which intersect in O.
Vertically opposite angles: тИа AOP =┬атИа BOQ
Vertically opposite angles: тИа COP =┬атИа DOQ
OP is the bisector of┬атИа AOC : тИа┬аAOP=┬атИа┬аCOP
Therefore, ┬атИаBOQ =┬атИа DOQ
Hence, OQ is the bisector of┬атИаBOD.