Question

$Q$ is a point on the side $SR$ of a $\Delta PSR$ such that $PQ=PR$. Prove that $PS>PQ$.

Answer 1

In $\Delta PSR,Q$ is a point on the side $SR$ such that $PQ=PR$.

To Prove:

$PS>PQ$

Proof:

From $\Delta PRQ$,

$PR=PQ$ (given)

$\Rightarrow \angle PRQ=\angle PQR$ (opposite angles to equal sides are equal)

But $\angle PQR>\angle PSR$ (exterior angle of a triangle is greater than each of opposite interior angle)

$\Rightarrow \angle PRQ>\angle PSR$

$\Rightarrow PS>PR$ (opposite sides to greater angle is greater)

$\Rightarrow PS>PQ(asPR=PQ)$

Hence Proved.