Given :
AD = BC and ∠DAB = ∠CBA
(i) In △ ABD and △ BAC,
⇒ AD = BC (Given)
⇒ ∠DAB = ∠CBA (Given)
⇒ AB = BA (Common side)
∴ △ ABD ≅ △ BAC (By S.A.S. congruence rule)
Hence, proved that △ ABD ≅ △ BAC.
(ii) As,
△ ABD ≅ △ BAC,
We know that,
Corresponding parts of congruent triangles are equal.
∴ BD = AC (By C.P.C.T.)
Hence, proved that BD = AC.
(iii) As,
△ ABD ≅ △ BAC,
We know that,
Corresponding parts of congruent triangles are equal.
⇒ ∠ABD = ∠BAC (By C.P.C.T.)
Hence, proved that ∠ABD = ∠BAC.