Internet search, no wish to see Baidu Post
16 kinds of Pythagorean theorem proving method
https://jingyan.baidu.com/article/27fa7326e6038846f9271f46.html
quite interesting, it would create a method for it.
It can be considered a "know know why" the.
The figure
FIG method Pythagorean theorem proved ambition:
Any right triangle ABC, three sides a, b, c;
Auxiliary:
1, for the triangle inscribed circle center O, radius r, respectively, cut points J, K, L;
2, so that the operating point D ACBD is rectangular, for the point P, Q, so OPDQ rectangular;
Derivation:
OLM congruent triangles and BPM;
OLN AQN congruent with the triangle;
OPDQ triangle ABC is equal to the area of the rectangle,
And is equal to a rectangular area OJAQ + OPBK + OKCJ and
即a*b/2 = d*e = r*d+r*e+r*r
Known that a = e + r, b = d + r, c = d + e, so
a^2+b^2
=(e+r)^2+(d+r)^2
=e^2+d^2+2*(r*d+r*e+r*r)
c ^ 2 = (e + d) ^ 2 = e ^ 2 + d ^ 2 + 2 * d * and
a ^ 2 + b ^ 2 = c ^ 2 is proved.
Baidu paste method is also inscribed circle,
Using a + b = c + 2 * r, and a * b / 2 = r * r + r * c derived condition.
(a+b)^2=a^2+b^2+2a*b
(c+2*r )^2=c^2+4*(r*r+r*c)
a ^ 2 + b ^ 2 = c ^ 2 is proved.
And I'm thinking different, or master the idea of some more simple and efficient.
According to statistics, the Pythagorean theorem proving method may have hundreds, I sit idle, jungle mesh barrier , if the older generation we similarity is purely coincidental, stroke just laugh Tell me, huh, huh.
That is interesting to praise it ~ ~
