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Question
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
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Solution
Given: In the figure,
AB = AD, CB = CD
To prove: Δ ABC ≅ Δ ADC
∠B = ∠D
AC bisects angle DCB
Proof: In Δ ABC and Δ ADC,
AC = AC .............(common)
AB = AD .............(given)
CB = CD .............(given)
(i) ∴ Δ ABC ≅ Δ ADC .................(SSS aciom)
(ii) ∴ ∠B = D .................(c.p.c.t.)
∠BCA = ∠DCA
(iii) ∴ AC bisects ∠DCB
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