Mathematics question on geometry.?

Question

H and M are the midpoints of AB and CD respectively of a parallelogram ABCD. Prove that AM and CH trisect the diagonal BD.

Answer 1

Let AM intersect BD at T and CH intersect BD at R.
AMCH is a parallelogram since AH is parallel and congruent to MC. Hence, AM is parallel to CH. HenceAM bisects DR.

Thus, MT bisects DR: because if a line is parallele to one side of a triangle and passes through the midpoint of another, then it bisects the third side.
We have DT = TR
Similarly, CH bisects BT. Thus BR = TR
ie DT = TR = BR

Thus, CH and AM trisect BD
EDIT: I see they took your badge too answers geek. :(

Answer 2

let AM intersctBD at F and HC at L
MC and AH are equle and parallrl
hence AHCM is parallelogram
hence AM parallel HC
in triangle ABF
AH=HB
HL parallel AF
hence BL=LF---------(1)
in triangle DLC
DM=MC
MF parallel LC
hence
DF=FL------------------(2)
from (1) and (2)
DF=FL=LB
there for AM and CH trisect the diagonal BD