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AB is a straight line on which PB and AP sides are standing.
So,
in triangle AOP and BOP
OP is a bisector of angle APB and AB line.
then, angle APO= angle BPO (OP is the bisector of angle APB)
AO = OB (OP is perpendicular and bisector of AB)
and, angle AOP = angle BOP = 90 degree (OP perpendicular AB making right angle)
OP =OP (common )
then triangle AOP is congruent to triangle BOP.
hence proved that OP is the perpendicular bisector of AB.
So,
in triangle AOP and BOP
OP is a bisector of angle APB and AB line.
then, angle APO= angle BPO (OP is the bisector of angle APB)
AO = OB (OP is perpendicular and bisector of AB)
and, angle AOP = angle BOP = 90 degree (OP perpendicular AB making right angle)
OP =OP (common )
then triangle AOP is congruent to triangle BOP.
hence proved that OP is the perpendicular bisector of AB.
jayasharma1:
how
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