Originally Posted by

**OnMyWayToBeAMathProffesor** hello,

i have to show that if the midpoints of consecutive sides of any quadrilateral are connected the result is a parallelogram.

i know the answer but do not know how to get it, help with explaining the process would be appreciated.

First point: $\displaystyle (0,0)$

Second Point: $\displaystyle (a,0)$

Third Point: $\displaystyle (b,c)$

Forth Point: $\displaystyle (d,e)$

I think the midpoints are right but i am not sure, i got them myself.

Midpoint of line A: $\displaystyle (a/2),0)$

Midpoint of line B: $\displaystyle ((a+b)/2),(c/2)$

Midpoint of line C: $\displaystyle ((b+d)/2),((c+e)/2))$

Midpoint of line D: $\displaystyle (d/2),(e/2)$

Here is where i get stuck, i do not know how to prove that the slopes of opposite sides are equal.

thank you.