Question 7
Laura won the local math olympiad and was awarded a "magical" ruler. With it, she can draw (as usual) lines in the plane, and she can also measure segments and replicate them anywhere in the plane. She can also divide a segment into as many equal parts as she wishes; for instance, she can divide any segment into 17 equal parts. Laura drew a parallelogram $A B C D$ and decided to try out her magical ruler. With it, she found the midpoint $M$ of side $C D$, and she extended side $C B$ beyond $B$ to point $N$ so that segments $C B$ and $B N$ were equal in length. Unfortunately, her mischievous little brother came along and erased everything on Laura's picture except for points $A, M$ and $N$. Using Laura's magical ruler, help her reconstruct the original parallelogram $A B C D$: write down the steps that she needs to follow and prove why this will lead to reconstructing the original parallelogram $A B C D$.