# ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that ∠ABD = ∠BAC.

$\mathrm{ABCD} \text { is a quadrilateral, where } \mathrm{AD}=\mathrm{BC} \text { and } \angle \mathrm{DAB}=\angle \mathrm{CBA}\\ \text { In } \triangle \mathbf{A B D} \text { and } \triangle \mathbf{B A C} \text { , }\\ \Rightarrow \mathbf{A D}=\mathbf{B C}\\ \Rightarrow \angle \mathrm{DAB}=\angle \mathrm{CBA} \quad[\text { Given }]\\ \Rightarrow \mathbf{A B}=\mathbf{B A} \text { [Common side] }\\ \triangle \mathbf{A B D} \cong \triangle \mathbf{B A C}\\ \angle \mathrm{ABD}=\angle \mathrm{BAC} [\mathrm{CPCT}]$