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Question

Let the line segments AB and CD intersect at O is such a way that OA=OB= OC, then AC= BD but AC may not be parallel to BD.
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A
True
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B
False
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Solution

The correct option is A True
It is given that,
AO=OD and CO=OB
Here, line segment AB and CD are concurrent.
So,
AOC=BOD [ Vertically opposite angle ]
Now,
In AOC and DOB,
AO=OD
CO=OD
AOC=BOD
AOCBOD [ By SAS property of congruence ]
AC=BD [ C.P.C.T ]
Here,
ACOBDO or OACOBD
Hence, there are no alternate angles, unless both triangles are isosceles triangle.
Hence, it is proved that, AC=BD but AC may not be parallel to BD.


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