Question

If $\Delta PQR$ is an isosceles triangle such that PQ=PR , then prove that the attitude PS from P on QR bisects QR

Answer 1

We have,

According to given figure.

$PQ=PR\left(giventhat\right)$

$QS=SR\left(Bydefinationofmidpo\mathrm{int}\right)$

$PS=PS\left(Commonline\right)$

Then,

$\Delta SPQ\cong \Delta SPR$ (BY congruency S.S.S.)

Hence, PS bisects $\angle PQR$ by definition of angle bisector.