Question

12. In the given figure, prove that:
(i) A AOD = A BOC
(ii) AD = BC
(iii) ZADB = ZACB
(iv) A ADB = A BCA
D
С
O
A
B​

Answer 1

Answer:

In ∆AOD and ∆BOC,

OA = OB (given)

∠AOD = ∠BOC (vertically opposite)

OD = OC (given)

(i) ∆AOD ≅ ∆BOC (by S.A.S)

(ii) AD = BC (c.p.c.t)

(iii) ∠ADB = ∠ACB (c.p.c.t)

(iv) ∆ADB ≅ ∆BCA

∆ADB = ∆BCA (given)

AB = AB (common)

∴ ∆ADB ≅ ∆BCA (Proved) .