9. ABCD is a trapezium in which AB || DC and its
diagonals intersect each other at the point O. Show
AO CO
that
BO DO
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Answer:
ABllDC,
Angle ABD=Angle BDC----(alternate interior angles)
Angle BAC= Angle ACD-----(alternate interior angles
In triangles AOB and COD
Angle ABD= Angle BDC-----(proved above )
Angle BAC= Angle ACD-----(proved above )
Angle AOB= Angle COD----(vertically opposite angles)
Therefore triangle AOB is congruent to triangle COD.
AO=CO------(by CPCT)
BO=DO----(by CPCT)
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