Question

In a triangle PQR, the bisector PS of angle P is perpendicular to side QR.
Show that triangle PQR is an isosceles triangle​

Answer 1

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.