Introduction to Pythagorean Theorem.

Pythagorean theorem is a basic geometric theorem, which means that the sum of the squares of two right angles of a right triangle is equal to the square of the hypotenuse. In ancient China, right-angled triangles were called Pythagorean Theorem, the smaller right-angled side was a hook, the other longer right-angled side was a chord, and the hypotenuse was a chord, so this theorem was called Pythagorean Theorem, and some people called it quotient height theorem.

There are about 500 ways to prove Pythagorean theorem, and Pythagorean theorem is one of the most proven theorems in mathematics. Pythagorean theorem is one of the important mathematical theorems discovered and proved by human beings in the early days. It is one of the most important tools to solve geometric problems with algebraic ideas, and it is also one of the ties of the combination of numbers and shapes.

2. Introduction to right triangle.

A right triangle is a geometric figure with a right angle. There are two kinds of right-angled triangles: ordinary right-angled triangles and isosceles right-angled triangles. It conforms to Pythagorean theorem and has some special properties and judgment methods. There are two situations, there are ordinary right-angled triangles and there are right-angled sides of isosceles right-angled triangles. The opposite side of a right angle is called a hypotenuse.

Special properties and judgement theorem of right triangle;

1 and the special properties of right triangle.

The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse. In a right triangle, the two acute angles are complementary. In a right triangle, the median line on the hypotenuse is equal to half of the hypotenuse (that is, the outer center of the right triangle is located at the midpoint of the hypotenuse, and the radius of the circumscribed circle R=C/2). This property is called the hypotenuse midline theorem of right triangle.

The product of two right angles of a right triangle is equal to the product of the hypotenuse and the hypotenuse height. In a right triangle, the height on the hypotenuse is the proportional average of the projection of two right-angled sides on the hypotenuse, and each right-angled side is the proportional average of the projection of this right-angled side on the hypotenuse. It is an important theorem of mathematical graphic calculation.

2. Right triangle judgment theorem.

A triangle with an angle of 90 degrees is a right triangle. If the opposite side of the 30 internal angle of a triangle is half of a certain side, the triangle is a right triangle with this long side as the hypotenuse. A triangle with two complementary acute angles (the sum of the two angles is equal to 90) is a right triangle.