Proof: Grade 28 Mathematics (East China Normal University Edition) Note: Similar congruence cannot be used for proof.

This problem was originally a geometric problem proved by congruence, and here it is explained that it cannot be proved by similar congruence.

Doubt: Did you learn anything similar in grade two or eight?

Analysis method (I don't know if I have learned it-it refers to the specific method rather than the name of the method):

1。 Establish a rectangular coordinate system with B as the origin, let the side length of the square be 2, and the F coordinate (x, x),

Then: (x+2) 2+(x-2) 2 = x 2+(x+1) 2+5.

Solution: x= 1

A little more.

2。 Establish a rectangular coordinate system with B as the origin, let the side length of the square be 2, the F coordinate (x, x), BE=m,

Then: (x+2) 2+(x-2) 2 = x 2+(x+m) 2+(2-m) 2+4.

Solution: x=2-m

So ed 2 = ef 2 = 4+(2-m) 2.

Intercept AN=2-m on AD

Then en 2 = BF 2 = 2 * (2-m) 2.