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Step-by-step explanation:
Given:-
AP = BQ
∠OAP = ∠OBQ = 90°
(i)
To prove:-
ΔOAP ≅ ΔOBQ
Solution:-
In ΔOAP and ΔOQB,
(i) AP = BQ (∵ Given)
(ii) ∠OAP = ∠OBQ (∵ Given)
(iii) ∠AOP = ∠BOQ (∵ Vertically opposite Angles are equal)
∴ ΔOAP ≅ ΔOBQ, by AAS Congruence Rule.
Hence Proved.
(ii)
Yes, OA = OB.
Since, ΔOAP ≅ ΔOBQ.
By CPCT, it is proved that OA = OB.
Hence Proved.
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