Draw a triangle ABC and two of its medians AM and BN. Let G be the point where AM intersects BN. Extend AM to the point P that makes GM- MP. Extend BN to the point Q that makes GN NQ 

(a) Explain why BG must be parallel to PC, and AG must be parallel to QC.

(b) What kind of a quadrilateral is PCQG? How do you know? 

(c) Find two segments in your diagram that must have the same length as BG. 

(d) How do the lengths of segments BG and GN compare?