Q. 104.3( 9 Votes )
Given: AO = OD and CO = OB
To prove: AC = BD
It is given that AO = OD and CO = OB
Here line segments AB and CD are concurrent.
∠AOC = ∠BOD …. As they are vertically opposite angles.
Now in ∆AOC and ∆DOB,
AO = OD,
CO = OD
Also, ∠AOC = ∠BOD
Hence, ∆AOC ≅ ∆BOD … by SAS property of congruency
AC = BD … by cpct
∠ACO ≠ ∠BDO or ∠OAC ≠ ∠OBD
Hence there are no alternate angles, unless both triangles are isosceles triangle.
Hence proved that AC=BD but AC may not be parallel to BD.
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