# Thread: Synthetic, Analytic, & Vector Proof

1. ## Synthetic, Analytic, & Vector Proof

Hello All:

I have to prove the Centroid theorem in synthetic, analytic, and vector techniques. My problem is, I do not understand how to even begin or these techniques. I have looked through all of my old geometry books (I am a college student) and nothing is really in them about these techniques. Is there any easy way that this can be explained? I am completely lost and have to have this done by Feb. 1st and feeling like I am in too deep

Thanks for any assistance.

2. ## synthetic proof

Draw triangle ABC with midpoints F, D and E.
Using the crossbar theorem, show point G is the intersection between two angles.
Draw the midpoints of AG and CG.
Find similar triangles FBD and ABC; and AGC and hiG, then congruent triangles hDi, and FDh.
Draw parallelogram FhiD. The diagonal properties of a parallelogram state they bisect each other. If two different verteces were choosen instead of the original chosen, you will find the same intersection of G.
and because point G is inside each angle,G is in the interior of triangle
ABC, proving point G is the centroid.