In the given figure ∠1 = ∠2 and AB = AC prove that: ∠B = ∠C

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asked 6 days ago in Class VII Maths by aditya23 (-854 points)

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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1 Answer

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answered 6 days ago by muskan15 (-2,499 points)

Proof:

In △ADB and △ADC,

 AB = AC (given)

∠I = ∠2 (given)

AD = AD (common)

∴ △ADB ≅ △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

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