# Showing that lines are concurrent using Pappus' theorem

I need to prove the following statement and I would really need help visualizing it. If someone could provide me with a picture, it would be extremely helpful.

"If A,B,D,E,N,M are six points such that the lines AE,DM,NB are concurrent and AM,DB,NE are concurrent, what can be said about the lines AB,DE,NM?"

Here, two straight lines, $a$ and $b$ are given. On $a$ there are some points $AE$, $DM$, and $NB$. On $b$ there are some other points $BD$, $EN$, and $AM$. Connect the points with the red, the yellow, and the blue lines called $D$, $E$, $B$, $A$, and $M$, $N$. (The letters used to denote the lines are the common letters of the notation of the points connected.) Then, $DE$ denotes the intersection of $D$ and $E$; $BA$ denotes the intersection of $B$ and $A$; and $MN$ denotes the intersection of $M$ and $N$. According to Pappus' theorem $DE$, $BA$, and $MN$ sit on a straight line called $c$.
Now, let's use the principle of duality and let $A$, $B$, $D$, $E$, $M$, $a$, $b$, and c, and $M$ denote points. Then, translate Pappus' theorem as shown below.