Question

In the adjoining figure, AB = AD and CB = CD.
Prove that ∆ABC ≅ ∆ADC.

Figure

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ AB=AD \\ CB=CD \\ \mathrm{To}\mathrm{prove}: \\ △ABC\cong △ADC \\ \mathrm{Proof}: \\ \mathrm{In}△ABC\mathrm{and}△ADC: \\ AB=AD\left(\mathrm{given}\right) \\ \mathrm{BC}=\mathrm{DC}\left(\mathrm{given}\right) \\ \mathrm{AC}=\mathrm{AC}\left(\mathrm{common}\right) \\ \therefore △ABC\cong △ADC(by\mathrm{SSS}\mathrm{congruence}\mathrm{property}) \end{gathered}$$