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In the Given Figure, Prove That: (I) ∆ Aod ≅ ∆ Boc (Ii) Ad = Bc (Iii) ∠Adb = ∠Acb (Iv) ∆ Adb ≅ ∆ Bca - Mathematics

Sum

In the given figure, prove that:
(i) ∆ AOD ≅ ∆ BOC
(ii) AD = BC
(iii) ∠ADB = ∠ACB
(iv) ∆ ADB ≅ ∆ BCA

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Solution

Proof:

In Δ AOD and Δ BOC 

OA = OB ........(given)

∠AOD = ∠BOC  .............(vertically opposite angles)

OD = OC ............(given)

(i) ∴ Δ AOD ≅ Δ BOC ................(S.A.S. Axiom)

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

and (iii) ∠ADB = ∠ACB .....(c.p.c.t.)

(iv) Δ ADB ≅ Δ BCA

Δ ADB = Δ BCA ..............(Given)

AB = AB .................(Common)

∴ Δ AOB ≅ Δ BCA

Hence proved.

Concept: Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
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APPEARS IN

Selina Concise Mathematics Class 7 ICSE
Chapter 19 Congruency: Congruent Triangles
Exercise 19 | Q 12
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