(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