Question

PQR is an equilateral triangle and S is any point in PR. Prove that QS > PS

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