MathDB

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; but 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

ABCD

and decided to try out her magical ruler; with it, she found the midpoint

M

of side

CD

, and she extended

CB

beyond

B

to point

N

so that segments

CB

and

BN

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

ABCD

: write down the steps that she needs to follow and prove why this will lead to reconstructing the original parallelogram

ABCD

Problem Statement