Question

In Δ PQR, if PQ=QR and L, M and N are the mid-point of the sides PQ, QR and RP respectively. Prove that LN=MN.

Answer 1

Explanation:

Given that in Δ PQR, PQ=QR and L, M and N are the mid-point of the sides PQ, QR and RP respectively.

We need to prove that LN = MN

Since, it is given that  PQ=QR

By the property of triangle, Angles opposite to the equal sides of a triangle are equal.

$\angle R=\angle P$

Thus, we have,

$\frac{1}{2} P Q=\frac{1}{2} Q R$

 $PL=MR$

Now, we shall consider the triangles Δ MRN and Δ LPN

$PL=MR$

$\angle R=\angle P$

Since, N is the midpoint of PR, we have,

$\mathrm{PN}=\mathrm{NR}$

By SAS property, we get,

$\triangle \mathrm{MRN} \cong \triangle \mathrm{LPN}$

Then by Corresponding Parts of Congruent Triangles theorem, we have,

$\mathrm{MN}=\mathrm{LN}$

Hence proved

Learn more:

(1) In triangle pqr if pq=qr and mid points of three sides pq, qr aand rp are l, m and n respectively. prove ln=mn

brainly.in/question/768545

(2) In ΔPQR, PQ = QR; L,M and N are the midpoints of the sides of PQ, QR and RP respectively. Prove that LN = MN.

brainly.in/question/7390829

Answer 2

Answer:

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