Question

 L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD, prove that DL, DK, BM and BN enclose a rhombus.​

Answer 1

Answer:

Let us first name the points of intersection of MB and DL as Q ; and of DK and NB as P.

Step-by-step explanation:

Now think of the whole figure as a symmetry around axis MK and also around axis NL. It becomes very obvious that every meeting point or point formed by intersection is equidistant from center of our square ABCD. So

DQ=QB=BP=PD. Now when all 4 sides of a quadrilateral are equal it has to be a rhombus at least, if not a square.