SOLUTION: Draw a triangle ABC, and let AM and BN be two of its medians, which intersect at G. Extend AM to the point P that makes GM = MP. Prove that PBGC is a parallelogram.

Algebra ->  Geometry-proofs -> SOLUTION: Draw a triangle ABC, and let AM and BN be two of its medians, which intersect at G. Extend AM to the point P that makes GM = MP. Prove that PBGC is a parallelogram.      Log On


   

Question 147483: Draw a triangle ABC, and let AM and BN be two of its medians, which intersect at G. Extend AM to the point P that makes GM = MP. Prove that PBGC is a parallelogram.
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
PROOF
As GM = MP, BM = MC and < BMG = < PMC, triangles BMG and PMC are congruent.
So < GBM = < MCP.
Thus BG is parallel to PC.
Similarly, we can show that GC is parallel to BP.
So PBGC is a parallelogram.