Question

PQR is an isosceles triangle where PQ = QR and S is the midpoint of QR. Prove that PS is the bisector of angle P​

Answer 1

Answer:

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.

Answer 2

Answer:

see the above attachment

Step-by-step explanation:

We have two triangles PQM and PRM.

PQ = PR [given]

QM = MR [M being the midpoint of QR]

PM is common to both.

Hence the two triangles PQM and PRM are congruent [By SSS postulate]

Therefore <QPM = <RPM [ angles opposite equal sides QM and MR], so PM bisects the <QPR.