Prove that: ∆ABC ≡ ∆ADC

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asked 4 days ago in Class VII Maths by muskan15 (-2,337 points)

Prove that:

(i) ∆ABC ≡ ∆ADC
(ii) B = D
(iii) AC bisects angle DCB

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1 Answer

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answered 4 days ago by aditya23 (-879 points)

Given : In the figure,

AB = AD, CB = CD

To prove : ∆ABC ≅ ∆ADC

∠B = ∠D

AC bisects angle DCB

Proof: In ∆ABC and ∆ADC,

AC = AC (common)

AB = AD (given)

CB = CD (given)

(i)  ∴ ∆ABC ≅ ∆ADC (SSS axiom)

∴ ∠B = D (c.p.c.t)

∠BCA = ∠DCA

∴ AC bisects ∠DCB

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