# Vector Proofs: A Quadrilateral thing!

1. Nov 10, 2005

### forevergone

Vector Proofs: A Quadrilateral thing #2!

Thanks lightgrav!

Last edited: Nov 10, 2005
2. Nov 10, 2005

### celticsthree4

re:

We had that problem on a geometry test in 9th grade, I will try digging it up and show you how ...if I can find it of course

3. Nov 10, 2005

### forevergone

Any help is always appreciated!

4. Nov 10, 2005

### lightgrav

you're given that dz = zb and az = zc , as your starting point.

What sums and differences of these equations show what you want?

5. Nov 10, 2005

### forevergone

az + zb = ab
cz + zd = cd

but az = zb, cz = cd therefore ab = cd!

Bah! That took like 5 minutes to see when I was spending 5 hours worth of time on it.

Thanks!

6. Nov 10, 2005

### lightgrav

The key to this stuff is writing in symbols
JUST WHAT they tell you in words.

That's why everybody calls these things "Word Problems"!

7. Nov 10, 2005

### forevergone

But a new problem arises :\.

8. Nov 10, 2005

### Diane_

One way to do this is to show that you have a pair of congruent triangles. (There are actually several pair, but you only need one.) Remember the definition of a parallelogram - that'll give you the angles. There's one more property of parallelograms that will give you the sides that you need.

9. Nov 10, 2005

### forevergone

I need to do this through vector proofs, though. If I could use congruent triangles, I would've been long done this problem :).

10. Nov 11, 2005

### daniel_i_l

You just have to show that 1/2(dc+da) = 1/2db. that means that the middle of db touches the middle of ac. This is easy to prove. Start with the two equations:
db = da + ab
db = dc + cb
and try to solve for 1/2(dc+da) in terms of db.