Question

two line segment AB and CD intersect each other at O. Such that AO =OB and CO=OD. prove that AC =BD
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Answer 1

Answer:

Solution

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Correct option is A)

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

∴   △AOC≅△BOD                [ By SAS property of congruence ]

⇒  AC=BD                      [ C.P.C.T ]

Here,

∠ACO



=∠BDO or ∠OAC



=∠OBD

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.

Step-by-step explanation: