Question

10. In the given figure AB = DC, <ABC = <DCB.
Prove that
(i) ∆ABC = ∆DCB
(ii) <A = <D
(iii) AC = DB,​

Answer 1

Given,

Triangles ABC and DCB are right-angled at A and D respectively.

AC = DB To prove,

ΔABC = ΔDCB

Proof,

In ΔABC and ΔDCB: AC = DB (given)

BC = BC (common) ∠CAB = ∠BDC = 90°

From the RHS congruence property, ΔABC ≅ ΔDCB.

Answer 2

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Given,

Triangles ABC and DCB are right-angled at A and D respectively.

AC = DB To prove,

ΔABC = ΔDCB

Proof,

In ΔABC and ΔDCB: AC = DB (given)

BC = BC (common) ∠CAB = ∠BDC = 90°

From the RHS congruence property,

ΔABC ≅ ΔDCB.

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