Congruent triangles's decision theorem 1. Edge: Three edges correspond to the coincidence of two equal triangles.
2. Angle and edge: two triangles with equal included angles are congruent.
3. Angle and Angle: Two angles and their clamping edges correspond to the congruence of two triangles.
4. Corner edge: the opposite side of two angles, one of which corresponds to the congruence of two triangles.
5. hypotenuse and right-angled edge: hypotenuse and a right-angled edge correspond to the combination of two right-angled triangles.
Quadrilateral 1. Definition of parallelogram: A quadrilateral with two groups of opposite sides parallel to each other is called a parallelogram.
2. The nature of parallelogram: the opposite sides of parallelogram are equal; The diagonals of parallelogram are equal; Diagonal bisection of parallelogram.
3. Determination of parallelogram: two groups of quadrangles with equal opposite sides are parallelograms; Quadrilaterals whose diagonals bisect each other are parallelograms; Two groups of quadrangles with equal diagonal are parallelograms; A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.
4. The midline of the triangle is parallel to the third side of the triangle, which is equal to half of the third side.
5. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
6. Definition of rectangle: a parallelogram with a right angle.
7. The nature of the rectangle: all four corners of the rectangle are right angles; The diagonals of a rectangle are equally divided. AC=BD
8. Rectangular judgment theorem: a parallelogram with a right angle is called a rectangle; Parallelograms with equal diagonals are rectangles; A quadrilateral with three angles at right angles is a rectangle.
9. Definition of diamond: parallelogram with equal adjacent sides.
10. 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.
The judgement theorem of 1 1. rhombus: A set of parallelograms with equal adjacent sides is a rhombus; Parallelograms with diagonal lines perpendicular to each other are rhombic; A quadrilateral with four equilateral sides is a diamond.
S diamond = 1/2×ab(a and B are two diagonal lines).
12. Definition of a square: a rhombus with right angles or a rectangle with equal adjacent sides.
13. 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.
14. Square judgement theorem: 1. A rectangle with equal adjacent sides is a square. Diamonds with right angles are squares.
15. Definition of trapezoid: A set of quadrangles with parallel opposite sides and another set of non-parallel opposite sides is called trapezoid.
16. Definition of right-angled trapezoid: a trapezoid with a right angle.
17. Definition of isosceles trapezoid: isosceles trapezoid.
18. Properties of isosceles trapezoid: two angles on the same base of isosceles trapezoid are equal; The two diagonals of an isosceles trapezoid are equal.
19. Judgment theorem of isosceles trapezoid: A trapezoid with two equal angles on the same base is an isosceles trapezoid.
Generally, a function in the form of y=kx+b(k, b is a constant, k≠0) is called a linear function, where x is an independent variable. When b=0, the linear function y=kx, also known as the proportional function.
Images and properties of linear functions
Any point P(x, y) on 1. linear function satisfies the equation: y = kx+b.
2. The coordinate of the intersection of the linear function and the Y axis is always (0, b), and the coordinate of the intersection of the linear function and the X axis is always (-b/k, 0).
3. The image of the proportional function always passes through the origin.
4. The relationship between k, b and the quadrant where the function image is located:
When k>0, y increases with the increase of x; When k < 0, y decreases with the increase of x.
When k>0, b>0, the straight line passes through the first, second and third quadrants;
When k>0, b<0, the straight line passes through the first, third and fourth quadrants;
When k < 0, b>0, a straight line passes through the first, second and fourth quadrants;
When k < 0, b<0, a straight line passes through the second, third and fourth quadrants;
When b=0, the straight line passing through the origin o (0 0,0) represents the image of the proportional function.
At this time, when k>0, the straight line only passes through the first and third quadrants; When k < 0, the straight line only passes through the second and fourth quadrants.
Data analysis 1. 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.
2. 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 the median of 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.
3. The data with the highest frequency in a set of data is the pattern of this set of data.
4. The difference between the maximum data and the minimum data in a set of data is called the extreme range of this set of data.
5. The greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation and the more stable it is.