Question

In the adjacent figure $△ABC$ is isosceles as $\overline{AB}=\overline{AC},\overline{BA}$ and $\overline{CA}$ are produced to $Q$ and $P$ such that $\overline{AQ}=\overline{AP}$. Show that $\overline{PB}=\overline{QC}$

Answer 1

Consider $△PAB$ and $△QAC$

$\overline{PA}=\overline{QA}$ ..... [given]

$\overline{AB}=\overline{AC}$ ...... [given]

$\angle PAB=\angle QAC$ ...... [vertically opposite angles]

$\therefore$ By SAS Congruency Rule,

$△PAB\cong △QAC$

So, $\overline{PB}=\overline{QC}$ ....... [By CPCT]