# Vector Proof

1. Oct 26, 2004

### vg19

Hey,

I am struggling with one question in vector proofs.

If D, E, and F are the midpoints of the sides of a triangle ABC, prove that
OD + OE + OF = OA + OB + OC

I dont really understand what we are trying to prove here. My first thought was that from some origin, to the points D E and F added up, is the same distance from some origin to A B and C added up.

I would really apprcieate some help. Also are there any tips or techniques you can give for generally solving questions that ask for proof?

Thanks

2. Oct 26, 2004

### Leong

is the equation in vector notation or it is a normal algebra equation ?

3. Oct 26, 2004

### vg19

vector notation...sorry couldnt draw the arrows, and acutally i do have 1 more qusetion that I ma not getting an answer to,

Prove that if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.

Ive been able to start saying that

AB must be parallel and equal to DC
AD must be parallel and equal to BC

However, im not sure how to prove this.

Any help is apprcieated

4. Oct 26, 2004

### Leong

$$let\ A(a_x,a_y), B(b_x,b_y), C(c_x,c_y)$$
$$find\ \vec{OA}+\vec{OB}+\vec{OC}$$in terms of $$\hat{i} \ and \hat{j}$$
find the coordinate of D,E and F using the midpoint formula in term of the coordinates of A, B or C and find
$$find\ \vec{OD}+\vec{OE}+\vec{OF}$$in terms of $$\hat{i} \ and \hat{j}$$

You should get the same result.
I have tried it.

Last edited: Oct 26, 2004