# Geometry proof

1. Oct 12, 2008

### lax1113

The line segments joining the midpoints of the opp. sides of a quadrilateral biset each other.

2. Relevant equations

3. The attempt at a solution
When I try to prove this for a parallelogram or a rectangle, it seems really obvious. Any number of ways can show this, by using triangles that are similar (using values of x1 and x2.. y1, y2), or simply just for the fact that since the opp are parallel that they have to be equal because if they weren't, the other set of lines could not be parallel. However, I can't find a way to PROVE that it would work for some other quadrilaterals like trapezoids and some of the funky looking ones. I would appreciate a little bump in the right direction, especially since we dont really deal with proofs in my class, its mostly applied math.

2. Oct 13, 2008

### Gib Z

Use co-ordinate geometry methods:

An arbitrary quadrilateral is described the the points (0,0) (0,a) (b,c) (d,e). Find expressions for the midpoints, and hence the equations of the line segments. Also find the midpoint of line segments and use the equations to show the other line passes through as well.

3. Oct 13, 2008

### lax1113

Thank you gib. I got it now.