Question

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.

Answer 1

It is given that

and L, M, N are the mid points of sides, , and respectively.

We have to prove that

Now using the mid point theorem, we have

And

Similarly we have

In triangle and we have

(Proved above)

(Proved above)

And (common)

So, by congruence criterion, we have

And

Then

HenceProved.