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In the Given Figure ; ∠1 = ∠2 and Ab = Ac. Prove That: (I) ∠B = ∠C (Ii) Bd = Dc (Iii) Ad is Perpendicular to Bc. - Mathematics

Sum

In the given figure ;
∠1 = ∠2 and AB = AC.
Prove that:
(i) ∠B = ∠C
(ii) BD = DC
(iii) AD is perpendicular to BC.

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Solution

Proof:
In Δ ADB and Δ ADC,
AB = AC .........(given)
∠1 = ∠2 ............(given)
AD = AD .............(common)
∴ Δ ADB ≅ Δ ADC ................(S.A.S. Axiom)

(i) Hence ∠B = ∠C ..............(c.p.c.t.)

(ii) BD = DC ...............(c.p.c.t.)

(iii) and ∠ADB = ∠ADC ............(c.p.c.t.)
But ∠ADB + ∠ADC = 180° ....(Linear pair)
∴ ∠ADB = ∠ADC = 90°
Hence AD is perpendicular to BC.

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 8
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