# Plane Proof

1. May 26, 2014

### mill

1. The problem statement, all variables and given/known data

Let A, B, C be the vertices of a triangle in the plane and let a, b, c be respectively, the midpoints of the opposite sides. Show that Aa+ Bb+ Cc = 0 (all of them have vector signs on the left).

2. Relevant equations

definition of plane

3. The attempt at a solution

Drew the picture which would look like a triangle within a triangle. The form Aa... looks most like the component equation but I don't understand how a, b, c equates to x, y, z.

2. May 26, 2014

### LCKurtz

You say a,b,c are midpoints of sides then you say they are vectors?? If everything is a vector what does Aa mean? And what are x,y,z? You need to state your problem more carefully.

3. May 27, 2014

### mill

That is exactly how the problem appears as written by the professor. A, B, and C form a triangle with a, b, c as midpoints. I meant that in the equation for example Aa has a vector sign hovering over it, but I don't know how to type in that symbol.

4. May 27, 2014

### LCKurtz

OK, so you mean $\vec{Aa}+\vec{Bb} +\vec {Cc} = \vec 0$. Here's a hint:$$\vec{Aa} = \vec{AB} +\frac 1 2 \vec{BC}$$and similarly for the other two.

5. May 27, 2014

### mill

Got it thanks.

Last edited: May 27, 2014