Question

In triangle PQR,PQ equal to PR and S is any point on PR.prove RS is less than QS

Answer 1

given : pq=pr
let s be any point on the side pr
to prove: qs>St
proof: angle q is equal to angle r ( isosceles triangle property)
but as angle sqr is lesser than angle q and hence it is also lesser than angle r .
so side opposite to greater angle is larger so side opposite to angle r is greater which is qs,
since angle sqr is lesser than angle r so side opposite to angle sqr i.e. sr is lesser than qs.
hence proved