(1) What is the angle of drawing the bisector ∠AEB of ∠MAB and ∠NBA at point E?
(2) After passing point E, make a straight line through AM in D and BN in C, and observe line segments DE and CE. What did you find?
(3) No matter how the two ends of DC move in AM and BN, does the value of AD+BC change as long as DC passes through point E? And explain why.
If point e is EF‖AM, then EF‖BN and AB are at point F.
Ae and be are bisectors.
∴∠3=∠4,∠ 1=∠2
Ae and be are bisectors.
∴∠AEF=∠3,∠ 1=∠EFB
∴EF=AF=BF
∴F is the midpoint of AB
E is the midpoint of Washington.
∴DE=CE？
∴EF= 1/2(AD+BC)
∴AB=AD+BC