(1) Solve the first problem by using the definition of external angles of triangles, the sum of internal angles of triangles and the properties of isosceles right triangles;

(2) It is proved that △ABD and △DCE are similar, and the functional relationship between Y and X can be obtained by using the similar properties of triangles;

(3) Based on the similarity between △ABD and △DCE, discuss and solve the problem in three situations: AD=AE, AD=DE and AE=DE.

explain

Solution:

( 1)

Guess ∠BDA=∠CED.

Prove:

AB = AC，∠BAC=90

∴∠B=∠C=45

∠∠ADC =∠b+∠ 1 = 45+∠2

∴∠ 1=∠2

∠∠BDA = 180-∠ 1-∠B，∠CED= 180 -∠2-∠C

∴∠ced=∠bda；

(2)

From (1):

∠BDA=∠CED，∠B=∠C

∴△ABD∽△DCE

∴BD/CE=AB/DC

Namely:

x/(4-y)=4/(4√2-x)

∴y=( 1/4)x？ -√2x+4(0