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(1) proves that in a square ABCD, AB=BC=AD=2, ∠ ABC = 90,

∫△BEC rotates 90 counterclockwise around point B to get △ △ABF,

∴△ABF≌△CBE，

∴∠FAB=∠ECB,∠ABF=∠CBE=90，AF=CE

∴∠AFB+∠FAB=90，

∵ Line segment AF rotates 90 clockwise around point F to get line segment FG.

∴∠AFB+∠CFG=∠AFG=90，

∴∠CFG=∠FAB=∠ECB，

∴EC∥FG，

AF = CE，AF=FG，

∴EC=FG，

∴ Quadrilateral EFGC is a parallelogram,

∴ef∥cg；

(2) solution: AD = 2, e is the midpoint of AB,

(1) proves that in a square ABCD, AB=BC=AD=2, ∠ ABC = 90,

∫△BEC rotates 90 counterclockwise around point B to get △ △ABF,

∴△ABF≌△CBE，

∴∠FAB=∠ECB,∠ABF=∠CBE=90，AF=CE

∴∠AFB+∠FAB=90，

∵ Line segment AF rotates 90 clockwise around point F to get line segment FG.

∴∠AFB+∠CFG=∠AFG=90，

∴∠CFG=∠FAB=∠ECB，

∴EC∥FG，

AF = CE，AF=FG，

∴EC=FG，

∴ Quadrilateral EFGC is a parallelogram,

∴ef∥cg；

(2) solution: AD = 2, e is the midpoint of AB,

Extended data:

Pythagorean theorem is a basic geometric theorem, which means that the sum of the squares of two right angles of a right triangle is equal to the square of the hypotenuse. In ancient China, right-angled triangles were called Pythagorean Theorem, the smaller right-angled side was a hook, the other longer right-angled side was a chord, and the hypotenuse was a chord, so this theorem was called Pythagorean Theorem, and some people called it quotient height theorem.

There are about 500 ways to prove Pythagorean theorem, and Pythagorean theorem is one of the most proven theorems in mathematics. Pythagorean theorem is one of the important mathematical theorems discovered and proved by human beings in the early days. It is one of the most important tools to solve geometric problems with algebraic ideas, and it is also one of the ties of the combination of numbers and shapes.

Baidu encyclopedia-Pythagorean theorem