Question

In ∆ PQR, PQ = QR, L,M and N are the mid point of the sides of PQ, QR and RP respectively prove that LN = MN

Answer 1

PQ = QR [data] 

∠P = ∠R 

In ∆ PLN and RMN 

PL = RM 

[PQ=QR and L and M are the midpoints] 

∠P = ∠R 

PN = NR [N is the mid point of PR] 

∴ ∆ PLN ≅ ∆RMN [SAS postulate] 

∴LN = MN [Corresponding sides]