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**Logic** We are given a hexagon as shown in the picture below and K, P, L, Q, M, R are the midpoints of AB, BC, CD, DE, EF and FA respectively. Proove that the triangles KLM and PQR have the same median point.

It is suggested in the textbook that if G1 and G2 are the median points of KLM and PQR to proove that vector OG1 equals vector OG2 for any point O.

Now, I know that OG1 for example would equal one third of the three vectors with beginning O and ends K, L and M. The same goes for G2 and P, Q and R.