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 $CD$.