Question

In the given figure, triangles ABC and DCB are right-angled at A and D respectively and AC = DB. Prove that ∆ABC ≅ ∆DCB.

Figure

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{Triangles}ABCandDCB\mathrm{are}\mathrm{right}\mathrm{angled}\mathrm{at}A\mathrm{and}D,\mathrm{respectively}. \\ AC=DB \\ \mathrm{To}\mathrm{prove}:△ABC\cong △DCB \\ \mathrm{In}△ABC\mathrm{and}△DCB: \\ \angle CAB=\angle BDC(90°\mathrm{each}) \\ BC=BC\left(\mathrm{common}\right) \\ AC=DB\left(\mathrm{given}\right) \\ \mathrm{B}y\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{congruence}\mathrm{property}: \\ △ABC\cong △DCB \end{gathered}$$