1 Prove that the triangle is a right triangle. It is helpful for you to remember cosine theorem, which is a special case of cosine theorem. At the beginning of China's earliest mathematical work "Parallel Calculation of Classics in Weeks", there was a dialogue in which Duke Zhou asked Shang Gao for mathematical knowledge. Duke Zhou asked, "I heard that you are very proficient in mathematics. I would like to ask: the sky can't get up without a ladder, and the ground can't be measured without a ruler. So how can we get data about heaven and earth?" Shang Gao replied: "The number comes from the understanding of the other party and the circle." There is a principle: when the moment of a right triangle gets a right-angled side' hook' equal to 3 and the other right-angled side' chord' equal to 4, then its hypotenuse' chord' must be 5. This truth was summed up when Dayu was in charge of water conservancy. "From the above conversation, we can clearly see that people in ancient China discovered and applied the pythagorean theorem, an important principle of mathematics, thousands of years ago. Readers who know a little about planes are well aware that the so-called Pythagorean theorem means that in a right triangle, the sum of the squares of two right-angled sides is equal to the square of the hypotenuse. Pythagorean Theorem is called Pythagorean Theorem in the west. The right triangle is represented by hook (A) and chord (B), and the hypotenuse is represented by chord (C). In fact, this mathematical theorem was discovered and applied in ancient China much earlier than Pythagoras. If it can't be verified that Dayu's flood control is a long time ago, then the dialogue between Duke Zhou and Shang can be determined in the Western Zhou Dynasty around 1 100 BC, more than 500 years earlier than Pythagoras. Hooking 3 strands, 4 strings and 5 strings is a special application of Pythagorean theorem (32+42=52). So it should be very appropriate to call it Pythagorean Theorem in the field of mathematics now. In the later book "Nine Chapters of Arithmetic", Pythagorean Theorem got a more standardized general expression. The book Gou Gu Zhang said: "Multiply the hook and the butt of the gun separately, then add up their products, and then open the square to get the rope." Make this passage into an equation, that is, chord = (hook 2+ strand 2)( 1/2), that is, the theorem of c=(a2+b2)( 1/2): if the two right angles of a right triangle are A and B respectively and the hypotenuse is C, then the square of A+the square of B = the two right angles of a right triangle. If the three sides A, B and C of a triangle satisfy A 2+B 2 = C 2, for example, a right-angled side is 3, a right-angled side is 4, and the hypotenuse is 3*3+4*4=X*X, and X=5. Then this triangle is a right triangle. (called the inverse theorem of Pythagoras theorem) Source: Pythagoras tree is a basic theorem, which was traditionally proved by Pythagoras in ancient Greece. It is said that after Pythagoras proved this theorem, he beheaded a hundred cows to celebrate, so it is also called "Hundred Cows Theorem". In China, Zhou Kuai Shu Jing recorded a special case of Pythagorean Theorem, which was reportedly discovered by Shang Dynasty's Shang Dynasty, so it is also called Shang Gao Theorem. Zhao Shuang in the Three Kingdoms period made detailed comments on Pythagorean Theorem as proof in Zhou Bi suan Jing. France and Belgium are called donkey bridge theorem, and Egypt is called Egyptian triangle. In ancient China, the shorter right angle side of a right triangle was called a hook, the longer right angle side was called a chord, and the hypotenuse was called a chord. Article source: original link:/content/383551851.html.

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