In an isosceles triangle PQR with PQ = PR, D and E are the points on QR, such that QE= RD, show that PD=PE

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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.