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ABCD is a quadrilateral in which AD = BC and \angle DAB =\angle CBA

Option: 1

\triangle A B D \cong \triangle B A C \\


Option: 2

B D=A C


Option: 3

\\ \angle A B D=\angle B A C


Option: 4

All of the above


Answers (1)

best_answer

\\\text{In } \triangle A B D\text{ and } \triangle B A C,\text{ we have} \\\\ A D=B C \quad \text { (given) } \\ \\\angle D A B=\angle C B A \quad \text { (given) }

\quad A B=B A \quad\text{( common )} \\\\ \therefore \quad \triangle A B D \cong \triangle B A C \quad(\text { SAS-criteria })

\begin{array}{l} \therefore \quad B D=A C \quad(\text { c.p.c.t. }) \\ \\\text { And, } \angle A B D=\angle B A C \quad \text { (c.p.c.t.) } \end{array}

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Kuldeep Maurya

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