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Question:

ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA. Prove that (i) ΔABD ≅ ΔBAC (ii) BD=AC (iii) ∠ABD=∠BAC

Solution:

In ΔABD and ΔBAC,
AD=BC (Given)
∠DAB=∠CBA (Given)
AB=BA (Common)
∴ ΔABD ≅ ΔBAC (By SAS congruence rule)
∴ BD=AC (By CPCT)
And, ∠ABD=∠BAC (By CPCT)