The definition of Pythagorean theorem in junior high school mathematics: the sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse;
Representation: If the two right angles of a right triangle are A and B and the hypotenuse is C, then.
The origin of Pythagorean theorem: Pythagorean theorem, also known as quotient height theorem, is called Pythagorean theorem in the west. In ancient China, the shorter right-angled side of a right-angled triangle was called a hook, the longer right-angled side was called a chord, and the hypotenuse was called a chord. As early as 3000 years ago, Shang Gao, a mathematician in Zhou Dynasty, put forward the Pythagorean theorem in the form of "hook three, string four and string five". Later, people further discovered and proved that the relationship among the three sides of a right triangle is the sum of two right angles.
Pythagorean theorem knowledge point 1. There is one and only one straight line when crossing two points.
2. The line segment between two points is the shortest.
3. The complementary angles of the same angle or equal angle are equal.
4. The complementary angles of the same angle or equal angle are equal.
5. There is one and only one straight line perpendicular to the known straight line.
6. Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7. The axiom of parallelism passes through a point outside a straight line, and one and only one straight line is parallel to this straight line.
8. If two straight lines are parallel to the third straight line, the two straight lines are also parallel to each other.
9. The same angle is equal and two straight lines are parallel.
10. The internal dislocation angles are equal and the two straight lines are parallel.
1 1. The inner angles on the same side are complementary and the two straight lines are parallel.
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 the long side. If they are equal, then a triangle with three sides A, B and C is a right triangle. If, when, a triangle with a, b and c as three sides is an obtuse triangle; If, when, a triangle with a, b and c as three sides is an acute triangle;
(2) The sum of A, B, C in the theorem is only an expression and cannot be considered unique. If three sides of a triangle meet the requirements of A, B and C, then a triangle with three sides of 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.