Question

In the figure 3.15 seg BQ $\cong$ seg PC and $\angle$APC = $\angle$AQB = 90$°$. Find the missing information, which is sufficient to prove
(i) $∆$APC $\cong$ $∆$AQB by Hyp-side theorem
(ii) $∆$APC $\cong$ $∆$AQB by SAA test.

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{seg}\mathrm{BQ}\cong \mathrm{seg}\mathrm{PC},\mathrm{i}.\mathrm{e}.\mathrm{BQ}=\mathrm{PC} \\ \angle \mathrm{APC}=\angle \mathrm{AQB}=90° \\ \left(\mathrm{i}\right)△\mathrm{APC}\cong △\mathrm{AQB}(\mathrm{by}\text{hypotenuse}-\mathrm{side}\mathrm{theorem}) \\ \mathrm{The}\mathrm{requirment}\mathrm{is}\mathrm{AC}=\mathrm{AB}. \\ \left(\mathrm{ii}\right)△\mathrm{APC}\cong △\mathrm{AQB}\mathrm{by}\mathrm{SAA}\mathrm{test} \\ \mathrm{Nothing}\mathrm{required},\mathrm{as}\mathrm{we}\mathrm{know}\mathrm{that}\angle \mathrm{PAC}=\angle \mathrm{QAB}. \end{gathered}$$