*Answer :*

Given that,

In Δ *PQR*

PQ = QR

And,

L, M, and N are the mid points of PQ, QR and RP respectively

To prove: LM = MN

Construction: Join L and M, M and N and N and L

Proof: We have,

PL = LQ, QM = MR and RN = NP

Since, L, M and N are mid points of PQ, QR and RP respectively.

And, also PQ = QR

PL = LQ = QM = MR = = (i)

Using mid-point theorem, we have

MN ‖ PQ

And,

MN = PQ = MN = PL = LQ (ii)

Similarly, we have

LN ‖ QR

And,

LN = QR = LN = QM = MR (iii)

From equations (i), (ii) and (ii), we have

PL = LQ = QM = MR = MN = LN

Therefore, LN = MN

Hence, proved

*Rate this question :*

*How useful is this solution?We strive to provide quality solutions. Please rate us to serve you better.*

*Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic ExpertsDedicated counsellor for each student24X7 Doubt ResolutionDaily Report CardDetailed Performance Evaluationview all courses*

*RELATED QUESTIONS :*

Prove that the anRS Aggarwal & V Aggarwal - Mathematics

If the sides of aRD Sharma - Mathematics

D is any point onNCERT Mathematics Exemplar

In a triangle *RD Sharma - Mathematics*

In Δ *ABC**RD Sharma - Mathematics*

In Δ *PQR**RD Sharma - Mathematics*

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics

Prove that the peRD Sharma - Mathematics

In Fig. 10.25, <iRD Sharma - Mathematics

In a <span lang="RD Sharma - Mathematics