1. Definition: A function with the shape y = (k is a constant, k≠0) is called an inverse proportional function.

2. Other forms of xy=k (k is a constant, k≠0) all hold.

3. Image: The image of inverse proportional function belongs to hyperbola.

The image of inverse proportional function is both axisymmetric and centrally symmetric.

There are two axes of symmetry: straight lines y=x and y =-X, and the center of the axis of symmetry is the origin.

3. Properties: When k > 0, the two branches of hyperbola are located in the first quadrant and the third quadrant respectively, and the value of y decreases with the increase of the value of x in each quadrant.

When k < 0, the two branches of hyperbola are located in the second and fourth quadrants respectively, and the y value of each quadrant increases with the increase of x value. ..

4.| k |: two coordinate axes representing point-to-point on the inverse proportional function image.

A rectangular area surrounded by a vertical line segment and two coordinate axes.

Chapter 18 Pythagorean Theorem

1. Pythagorean Theorem: If the lengths of two right angles of a right triangle are A and B, and the length of the hypotenuse is C, then A2+B2 = C2.

2. The inverse theorem of Pythagorean theorem: If the lengths of triangle A, B and C satisfy A2+B2 = C2. Then this triangle is a right triangle.

A proposition that is proved to be correct is called a theorem.

We call two propositions with opposite topics and conclusions reciprocal propositions. If one of them is called the original proposition, then the other is called its inverse proposition. (Example: Pythagorean Theorem and Pythagorean Theorem Inverse Theorem)

Chapter 19 Quadrilateral

Definition of parallelogram: Parallelograms with two groups of parallel opposite sides are called parallelograms.

The nature of parallelogram: the opposite sides of parallelogram are equal;

Diagonal angles of parallelogram are equal.

Diagonal bisection of parallelogram.

Determination of parallelogram 1. Two sets of quadrilaterals with equal opposite sides are parallelograms.

2. The quadrilateral whose diagonal lines bisect each other is a parallelogram;

3. Two groups of quadrangles with equal diagonal are parallelograms;

4. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

The midline of the triangle is parallel to the third side of the triangle and equal to half of the third side.

The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse.

Definition of rectangle: a parallelogram with a right angle.

The nature of the rectangle: all four corners of the rectangle are right angles;

The diagonals of a rectangle are equally divided. AC=BD

Rectangular judgement theorem: 1. A parallelogram with a right angle is called a rectangle.

2. Parallelograms with equal diagonals are rectangles.

A quadrilateral with three right angles is a rectangle.

Definition of diamond: parallelogram with equal adjacent sides.

The nature of the diamond: all four sides of the diamond are equal;

The two diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals.

Decision theorem of diamond: 1. A set of parallelograms with equal adjacent sides is a diamond.

2. Parallelograms with diagonal lines perpendicular to each other are diamonds.

A quadrilateral with four equilateral sides is a diamond.

S diamond = 1/2×ab(a and B are two diagonal lines).

Definition of a square: a diamond with right angles or a rectangle with equal adjacent sides.

The essence of a square: all four sides are equal and all four corners are right angles. A square is both a rectangle and a diamond.

Square judgment theorem: 1. A rectangle with equal adjacent sides is a square. Diamonds with right angles are squares.

Definition of trapezoid: A set of quadrangles with parallel opposite sides and another set of quadrangles with non-parallel opposite sides are called trapezoid.

Definition of right-angled trapezoid: a trapezoid with a right angle.

Definition of isosceles trapezoid: isosceles trapezoid.

The nature of isosceles trapezoid: the two angles on the same base of isosceles trapezoid are equal;

The two diagonals of an isosceles trapezoid are equal.

Judgment theorem of isosceles trapezoid: two trapezoid with equal angles on the same base are isosceles trapezoid.

Auxiliary lines commonly used to solve trapezoidal problems are shown in the figure.

The center of gravity of the line segment is the midpoint of the line segment. The center of gravity of a parallelogram is the intersection of its two diagonals. The point of doubt when three center lines of a triangle meet is the center of gravity of the triangle. A rectangle with an aspect ratio (about 0.6 18) is called a golden rectangle.

Chapter 20 Data Analysis

1. Arithmetic average:

2. Weighted average: the calculation formula of weighted average.

Understanding of weight: It reflects the importance of a certain data in the whole data.

But in the form of ratio or percentage, the weighted average value is obtained by using the frequency distribution table.

3. Arrange a set of data in order from small to large (or from large to small). If the number of data is odd, the middle number is median); This set of data. If the number of data is even, the average of the middle two data is the median of this set of data.

4. The data with the highest frequency in a set of data is the pattern of this set of data.

5. The difference between the data in a set of data and the minimum data is called the range of this set of data.

6. The greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation and the more stable it is.

Data collection and sorting steps: 1. Data collection II. Data arrangement 3. Data description 4. Data analysis. Investigation report writing. Communication.

7. The average value is influenced by the extreme value, and the mode number is not influenced by the extreme value, which is an advantage. The calculation of median is rarely affected by extreme value.