Question

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

Answer 1

It is given that

And is the mid point of

So

And is the mid point of

So

And is the mid point of

So

We have to prove that

In we have

(Equilateral triangle)

Then

, and

, and

Similarly comparing and we have

, and

And (Since N is the mid point of )

So by congruence criterion, we have

Hence.