Question

If M and N are the mid-points of sides AB and DC of parallelogram ABCD, then prove

that AMCN is a parallelogram.​

Answer 1

DC and AB are opposite sides of a parallelogram. By the definition of a parallelogram they are equal in length. Let’s call the length x.

A midpoint is something that is at the middle of a line segment: it creates two smaller line segments equal in length.

AB = DC = x

AM = BM = x/2 (The midpoint divides the length of AB in half)

CN = DN = x/2 (The midpoint divides the length of CD in half)

AM and CN both equal x/2

AM = CN