32. Exemplar example problems III

1. In the below figure, \(PQ = PR\) and \(\angle Q = \angle R\). Prove that \(\triangle PQS \cong \triangle PRT\).

 

 

2. In the below figure, two lines \(AB\) and \(CD\) intersect each other at the point \(O\) such that \(BC \parallel DA\) and \(BC = DA\). Show that \(O\) is the mid-point of both the line-segments \(AB\) and \(CD\).