Question

In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ∆ABC such that AX = AY. Prove that CX = BY.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{AXC}\mathrm{and}△\mathrm{AYB},\mathrm{we}\mathrm{have}: \\ \mathrm{AC}=\mathrm{AB}\left(\mathrm{Given}\right) \\ \mathrm{AX}=\mathrm{AY}\left(\mathrm{Given}\right) \\ \angle \mathrm{BAC}=\angle \mathrm{CAB}(\mathrm{Angle}\mathrm{common}\mathrm{to}△\mathrm{AXC}\mathrm{and}△\mathrm{AYB}) \\ \therefore △\mathrm{AXC}\cong △\mathrm{AYB}(\mathrm{SAS}\mathrm{criterion}) \\ \mathrm{So},\mathrm{CX}=\mathrm{BY}\left(\mathrm{CPCT}\right) \end{gathered}$$
Hence, proved.