英文四邊形數學題5(20分)

(a)
Consider triangle ADG and triangle ABF
Since DG // BF, so triangles ADC and triangle ABF are similar.
Since AD:AB=1:2, so AG:AF=1:2, or AG=GF
Consider triangle CEH and triangle CBF
Since EH // BF, so triangles CEH and triangle CBF are similar
Since CE:CB=1:2, so CH:CF=1:2, or CH=HF

Since F is mid point of CA, so AF=FC, and therefore,
AG=GF=FH=HC
(b)
Consider triangle AMF & triangle AEH
MF//EH, so triangle AMF & triangle AEH are similar,
since AG=GF=AH, so AF:AH=2:3
Since triangle AMF & triangle AEH are similar,
so AM:AE=2:3
ME = AE - AM = AE - (2/3) AE = 1/3AE
ME:AE = 1:3