Two line segments AB and CD bisect each other at point O. Prove that:
(a) AAOC = ABOD.
(b) AC = BD
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1 thought on “Two line segments AB and CD bisect each other at point O. Prove that:<br />(a) AAOC = ABOD.<br />(b) AC = BD<br />​”

1. Answer:AB and CD bisect each other at O i.e, AO=BO and CO=DO

   in ΔCOA and ΔDOB

   Given CO=OD,∠COA=∠BOD [ vertically opp angles]

   AD=BD

   ∴ΔCOA≅ΔBOD

   (i) ∴AC=BD[C.P.CT]

   (ii) ∠CAB=∠ABD[C.P.CT]

   again

   in ΔCOB and ΔAOD

   CO=OD [given]

   BO=AO [given]

   ∠COB=∠AOD [vertically opp angles]

   ∴ΔCOB≅ΔAOD

   ∴∠CBA=∠BAD [ C.P. C.T]

   (iii) and so AD∣∣CD [ ∵∠CBA=∠BAD which are altanate angles]

   and AD=

   Step-by-step explanation:

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