Question

In fig. 3.1 and 3.2 seg AB $\cong$ seg AC, show that x = y.
(i) (ii)

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{seg}\mathrm{AB}\cong \mathrm{seg}\mathrm{AC} \\ \mathrm{In}\mathrm{both}\mathrm{the}\mathrm{figures},\mathrm{in}△\mathrm{ABC}, \\ \angle \mathrm{ABC}=\angle \mathrm{ACB}(\because \mathrm{seg}\mathrm{AB}\cong \mathrm{seg}\mathrm{AC})....\left(\mathrm{i}\right) \\ \mathrm{Also},x+\angle \mathrm{ABC}=180°(\text{l}\mathrm{inear}\mathrm{pair}) \\ \mathrm{and},y+\angle \mathrm{ACB}=180°(\text{l}\mathrm{inear}\mathrm{pair})....\left(\mathrm{ii}\right) \\ x\mathit{}=180°-\angle \mathrm{ABC} \\ \Rightarrow x=180°-\angle \mathrm{ACB}\left\{\mathrm{From}\left(\mathrm{i}\right)\right\} \\ \Rightarrow x\mathit{}=\mathit{}y\mathit{}\left\{\mathrm{From}\left(\mathrm{ii}\right)\right\} \end{gathered}$$