Mathematics
In the adjoining figure, ∠BCD = ∠ADC and ∠BCA = ∠ADB. Show that
(i) △ACD ≅ △BDC
(ii) BC = AD
(iii) ∠A = ∠B
Triangles
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Answer
(i) In △ACD and △BDC,
Given,
∠BCD = ∠ADC
∠BCA = ∠ADB
∴ ∠BCD + ∠BCA = ∠ADC + ∠ADB
⇒ ∠ACD = ∠BDC
CD = CD (Common).
∠ADC = ∠BCD (Given)
Hence, proved that △ACD ≅ △BDC by ASA axiom.
(ii) We know that, △ACD ≅ △BDC.
We know that corresponding sides of congruent triangles are equal.
∴ BC = AD.
Hence, proved that BC = AD.
(iii) We know that, △ACD ≅ △BDC.
We know that corresponding angles of congruent triangles are equal.
∴ ∠A = ∠B.
Hence, proved that ∠A = ∠B.
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