In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP respectively.

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In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP respectively. Prove that: LN = MN.

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Given that, in ΔPQR, PQ =QR and L,M,N are midpoints of the sides PQ, QP and RP respectively and given to prove that LN = MN

Here we can observe that PQR is and isosceles triangle

And also, L and M are midpoints of PQ and QR respectively

∴ ∠QPR and ∠LPN and ∠QRP and ∠MR are same

PN=NR              [∴ N is midpoint of PR]

So, by SAS congruence criterion, we have ΔLPN≅ΔMRN

⇒ LN=MN

[∴ Corresponding parts of congruent triangles are equal]