Pythagoras definition
In any right-angled triangle (RT△), the sum of squares of the lengths of two right-angled sides is equal to the square of the length of the hypotenuse, which is the Pythagorean theorem. That is, the square of the hook plus the square of the strand equals the square of the chord.
Pythagorean theorem is a special case of cosine theorem. This theorem is also called "the High Theorem" in China (it is said that Dayu will use this theorem to solve the calculation problems in water conservancy), and it is called "Pythagoras Theorem" or "Hundred Cows Theorem" abroad. (After Pythagoras discovered this theorem, he beheaded a hundred cows to celebrate, so it was also called "Hundred Cows Theorem"), and the French and Belgians also called this theorem "Donkey Bridge Theorem".
Pythagoras proved that
Make two congruent right-angled triangles, and let their two right-angled sides be A and B (B >; A), the hypotenuse is C. Make a square with a side length of C. Put them into the polygon as shown in the figure, so that E, A and C are in a straight line.
QP∨BC is the point passing through Q, and P is the point passing through AC.
Point B is BM⊥PQ, and the vertical foot is m; A little more.
F is FN⊥PQ, and the vertical foot is n.
∫∠BCA = 90, QP∨ BC.
∴ ∠MPC = 90，
* bm⊥pq，
∴ ∠BMP = 90，
∴ BCPM is a rectangle, that is ∠ MBC = 90.
∫∠QBM+∠MBA =∠QBA = 90，
∠ABC + ∠MBA = ∠MBC = 90
∴ ∠QBM = ∠ABC，
∵∠ BMP = 90，∠ BCA = 90，BQ = BA = c，
∴rtδbmq≌rtδBCA。
Similarly, RT δ QNF ≌ RT δ AEF can prove that A2+B2=C2.
Pythagoras' example
Example 1. It is known that ∠ Abd = ∠ C = 90, AC = BC, ∠ DAB = 30 and AD = 8. Find the length of BC.
The analysis first found AB in Rt△ABD, and then found BC in Rt△ACB.
When solving Rt△ABD,
∠∠ABD = 90，∠DAB=30，
From Pythagorean Theorem:
AB2=AD2-BD2=82-42=48。
In △ABC, ∠ c = 90, AC = BC.
∵AC2+BC2=AB2，
∴2BC2=48，
∴BC2=24，
Example 2. The hypotenuse of a right triangle is 2, and the sum of two right angles is 6. Find the area of this right triangle.
Let right angles be a and b,
∴a2+b2=4.
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Problems needing attention:
The premise of (1) Pythagorean theorem is right triangle;
(2) Solving the ordinary equations or equations in the problem;
(3) Given the length of two sides in a right triangle, to find the length of the third side, it is required to find out which one is the hypotenuse and which one is the right side. If you are not sure, we should discuss it in categories.
I hope I can help you and adopt it.