Question

ΔPQR is isosceles with PQ = PR. T is the mid-point of QR, and TM and TN are perpendiculars on PR and PQ respectively. Prove that,
PM = PN 

Answer 1

Since, ΔQNT ≅ ΔRMT
NQ = MR .............(ii)
But PQ = PR  .........(iii)  ...(given)
Subtracting (ii) from (iii)
PQ - NQ = PR - MR
⇒ PN = PM.