Pythagorean theorem formula 1 basic recipe
In a right-angled triangle on the plane, the square of the length of two right-angled sides adds up to the square of the length of the hypotenuse. If the lengths of two right-angled sides of a right-angled triangle are A and B, and the length of the hypotenuse is C, then the formula of Pythagorean theorem is a2+b2=c2.
2. Complete formula
a=m,b=(m^2/k-k)/2,c=(m^2/k+k)/2①
Where m≥3
(1) When m is determined to be any odd number greater than or equal to 3, k={ 1, and m 2 is less than all factors of m}
(2) When m is determined to be any even number ≥4, k = {all even factors less than m 2/2}
3. Commonly used formulas
(1) (3,4,5), (6,8,10) ... 3n, 4n, 5n (n is a positive integer).
(2) (5, 12, 13), (7,24,25), (9,40,4 1) ...2n+ 1，2n 2+2n，2n 2+2n+。
(3) (8, 15, 17), ( 12,35,37) ...2 2 * (n+ 1)，[2 (n+ 1)] 2-。
(4) m 2-n 2, 2mn, m 2+n 2 (m and n are positive integers, m >；; n).
Inverse Theorem of Pythagorean Theorem If the lengths a, b and c of three sides of a triangle are satisfied, then the triangle is a right triangle, where c is the hypotenuse.
① The inverse theorem of Pythagorean theorem is an important method to judge whether a triangle is a right triangle. It determines the possible shapes of triangles by "transforming numbers into shapes". When applying this theorem, the sum of squares of two small sides can be compared with the square of longer side C 2. If they are equal, then a triangle with three sides A, B and C is a right triangle. If a 2+b 2；; C 2, a triangle with three sides A, B and C is an acute triangle;
(2) In the theorem, A, B, C and A 2+B 2 = C 2 are only expressions and cannot be considered unique. If three sides of a triangle satisfy A 2+B 2 = C 2, then a triangle with three sides A, B and C is a right triangle, but B is the hypotenuse.
③ When the inverse theorem of Pythagorean Theorem is described by a problem, when the square of hypotenuse is equal to the sum of the squares of two right-angled sides, it cannot be said that this triangle is a right-angled triangle.