Question

in the adjoining figure , angle ABC = angle ACB , D and E are points on the sides AC and AB respectively such that BE=CD . prove that
i) triangle EBC =~ triangle DCB
ii) triangle OEB =~ triangle ODC
iii) OB=OC​

Answer 1

given:-. ∠ABC=∠ACB. , BE=CD

TO prove:-

i) triangle EBC =~ triangle DCB

ii) triangle OEB =~ triangle ODC

iii) OB=OC

proof :-

in tri(EBC) and tri(DCB)

∠EBC=∠DCB. ( given ,∠ABC=∠ACB)

BE=CD. (given)

BC=BC. (commen)

so , △EBC≡ △DCB. ( by SSS property). #######

now subtract commen ar(OBC) from both sides

△EBC - ar(OBC)≡ △DCB -ar(OBC)

△OEB ≡ △ ODC. ########

OB=OC ( by C.P.C.T. ). #######

#hence_proved

hope it'll help you

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Answer 2

Answer:

hope it helps you

It might be pretty easy for you than the other methods